Disclaimer
I did this run on a Powerpak. In case it matters for future reference, I used a ROM with checksum 36f9c268d5152085c914eb732392848e.

Run comments
For most of the games I have speedrun, I've also written a speedrun guide and then linked to it in the comments. I haven't done that for Beetlejuice, so I'll go a bit more into detail about how the game works in these comments instead.
The manual has a weird way of naming the stages, so I'm instead going to use the map screen showing up as indicating a new stage.

Stage 1 (town)
* The timing of the lights inside the first house is random, but within certain limits. I try to position myself in front of the left side of the fireplace and start running slightly after the lights turn on. This seems to hit some sort of average for getting through when the first two lights are off, but the majority of attempts still end from getting insta-killed by the lights. Because of Beetlejuice's slow acceleration, I don't find it better to stand right next to the lights and start running as soon as the lights turn off, although it's certainly possible as well.

* Ideally, I'd like to get the invincibility flower around the first switch. The flowers' appearing is completely random though and it's almost no time difference if you get the first one or not. The second flower is more of a time gain and I got one.

* Back on the outside, I need 25 more credits from the bugs to afford the skeleton scare. The spawning and movement of the bugs are completely random. A little time was lost due to chasing a bug, but it was still better than average.

* The boss fight is again pure randomness. With this route, I only have three attacks left and they all need to connect rapidly in order to defeat the boss. The majority of the boss's attack patterns make this impossible. Run to the right, attack, small jump to the right (and hope for the boss's attack to pass by below) and then two quick attacks seems to work the best for me (maybe one out of four in average?).

Stage 2 (sewers)
* The first two deaths on the octopuses are unavoidable with this route. The death animation from jumping into an enemy takes slightly longer than falling off the screen, so I try to do the latter for all the death abuses in this stage.

* A somewhat obscure game mechanics is that the game awards you a free umbrella scare if you have no scares at all when encountering a cave frog. The screen freezes at these points, which would mean a soft-lock unless the free scare appeared.

* The next two deaths against the cave frogs were avoidable. However, the cave frogs' attacks are random and very often result in getting hit. For consistency, I therefore decided to take these two optional deaths for a small time loss.

* The shop mechanics are odd. The content of each individual shop is completely determined, but depends on the x-position you enter the shop on. In my route, I need to visit this specific shop to get all the scares I need and I need to visit it twice in order to get scares from two different setups. There is an alternative that only visits the shop once. I could have bought another umbrella and birdman scare (for a total of 550) to use against the last cave frog and boss in this stage instead of buying the ogre scare (for a cost of 500). While this saves time from avoiding the second shop visit, it has a few downsides. 1) It requires 50 more credits (so not possible in this attempt without spending additional time farming money). 2) It would also require another trip to the menu at the boss in this stage. 3) Finally, and most importantly in my case, it adds quite a bit of risk to use the umbrella scare against the last cave frog (the ogre scare one-hit kills cave frogs, while other scares require 7 attacks). I think I timed out the difference to be around one second or so if everything went perfectly in favor of the one-visit option.

* Getting through the last octopus depends on the sub-pixel and it doesn't seem to be consistent from one time to the next. As far as I can tell, it's therefore not going to be possible to manipulate. The chance is 50/50 though and there is no execution difficulty involved (just hold A pressed down and Beetlejuice will jump on the first frame you have control over him after getting hit).

* The boss always throws slow attacks and you have more than enough scares, so this boss is much easier than the one in stage 1. There is still an RNG-element to it though. Depending on when it decides to attack, you can push it to the right wall in 3 or more attacks. I got a bad pattern in this attempt and had to use 4 attacks. The time difference is pretty minor though.

Stage 3 (basement, overhead)
Very short stage. The saws move in pre-determined patterns and start when you enter the room. So for once no RNG with these enemies.
I slowed down ever so slightly on the right side to avoid getting hit by the upper saw.

Stage 4 (house, overhead)
* The sweeper fight is one of the two most random and time-consuming elements in the run. I haven't figured out exactly how their movement is built up. But it seems to be one random component and one component that is somehow linked to Beetlejuice's movement/position. What's worse about this fight is that the potions used to defeat them are also random. Once you throw a potion, it will take off in one of several directions. Since you can't predict the initial direction, it's very much just hoping for the best.
My strategy is to try and get one hit on the left sweeper before the potion takes off in its random direction. Then I try to move up to the upper left room and lure all the sweepers in there. Having all the sweepers in one room obviously increases the chances of the potions hitting them, but also means being more exposed to taking hits from the sweepers. Once I have at least the two lower sweepers in the upper left room (far from guaranteed to happen), I move over to the right to stock up on potions and hopefully also avoid some damage. The plan worked out perfectly to begin with, but finishing off the last sweeper could have been a few seconds faster if the potions had cooperated more. Considering how RNG-dependent this fight is, it was still very good and I saved a chunk of time over the vast majority of attempts.

* In the next set of rooms, I got a bit of bad luck with the spiders and decided to take a hit that cost a life. I could have waited out the spider to avoid the hit, but I think it was still the right decision to take the death and press on instead of waiting for all of the spiders to get out of the way.

* The fight with Delia's art pieces (yellow room) is another RNG-fight. They only take two hits each though and the hammer is at least a predictable weapon, so it's usually not having too much of an impact on the time. It was a good fight this time, even though I missed catching the hammer at the end and had wait for it to bounce back.

* Since you have the hammer against the stools (at least I think that's what they're supposed to be?), the fight is similar to the one against the art pieces. Taking out the last stool is off-screen and can sometimes be messed up if it moves out of the way. It usually works if you manage to pin it down with a first hit though, like in this attempt. Overall, it was a quick fight this time.

Stage 5 (attic, overhead)
* The bathroom fight with the flies is the second of the two major RNG-elements of the run. The flies' movements have one component following the screen and one RNG-component. The latter is disabled for a short while if you collide with one of the flies. When this happens, it's possible to manipulate them to be in front of the fly swatter. My general strategy for this room is to throw the fly swatter as soon as I enter the room. Then I move over to the right side and finally catch and release the swatter vertically. This attempt went amazingly well and the flies went down so quickly that I didn't even need to change direction of the swatter.

* Chasing the mouse can be a time sink. This attempt went absurdly good. Getting the mouse quickly into the left room has a very low probability (well below 1%). Seeing this in a final run with already so many things going my way is extremely fortunate.

* In the next set of rooms with Lydia, there is unfortunately the biggest execution mistake in the run by mistiming handing over the necklace to her. This ended up costing 3 seconds.

* I got out this stage with 1 life and 1 continue (= 3 lives) left. Other than losing a life is a time loss, lives are usually a big concern at this point since I need a minimum of 3 lives for being able to do two death abuses in the final stage. Even on good attempts, where enemies are supposed to have gone down quickly, I often end up short on lives. Having 4 lives left is excellent and doesn't happen too often. Having even more lives left is definitely possible, but I can't recall that ever happened to me.

* At this point, the RNG has overall been extremely accommodating with all the major spots ranging from great to crazy good. The pace at this point was 10 seconds faster than any previous attempt I've had.

Stage 6 (graveyard)
Pretty tough stage with several sections requiring correct execution. Most attempts reaching this far end here.

* The entrance to the tower is activated even off-screen. The blind jump to it is completely consistent.

* Like all the invincibility flowers, the ones in the tower spawn randomly. Having the flower saves a bit of time, so I usually wait out the flower appearing by jumping back and forth. I lost around two seconds from jumping back-and-forth once. Quite often, I can actually get the flower on the first attempt, so I consider this to be a bit of bad luck. It could definitely have been far worse as well though.

* The hit against the boss was intentional. When you lose a scare, you automatically get rid of all the hit points, which is an advantage in the next stage. This does however slow down the boss fight by one jump. On top of that, I played very conservatively and it took four jump-attacks before the boss was defeated, instead of the usual three. The boss can be a bit tricky though and randomly uses the flash attack (-> losing the scare -> attempt over). With the right positioning, you can avoid the attacks and still keep attacking the boss. It requires fairly accurate placement and the extra caution was the reason for the additional jump needed.

Stage 7 (attic maze, overhead)
Once you know the route, this stage is basically just consisting of another sweeper fight. This one is easier since it's done in a much more confined area though. After having thrown the first potion, I teleport out of the way to avoid getting hit by the sweepers. I then teleport back to throw a second potion as soon as the first one wears out and then hope that it's enough to finish them off. That's far from guaranteed though. I had the right luck this time and the second potion took care of them as planned.

Stage 8 (afterlife)
The birdman scare allows for some creative shortcuts in this stage, which is actually pretty easy once you've learned the route. I will admit that the stage was played a bit conservatively though since most mistakes will be very costly and I had a feeling that this attempt was on a good pace.

* I took one hit against a frog on the right side. With the right screen positioning and jump timing, it's possible to run beneath the frogs, but I haven't found a consistent setup for it. Usually, I get hit by two frogs, so only getting hit by one was not that bad.

Final thoughts
Once my routes started to settle and I had a few decent completed attempts to use as reference, I felt that a low 11:4x would be a realistic goal. I was secretly hoping for an 11:3x though. So seeing a time of 11:29 for this run was a surprise to say the least.
Lately, I've had several attempts on a good pace (most of them ended in the graveyard stage). This attempt was 10 seconds faster than my previously best attempt getting into the graveyard stage (at which point most of the RNG is in the past). So I'm very happy that I was able to make a completed run out of it and I consider it more or less a one of a kind for the current knowledge and skillset I have in this game.
But if anyone out there is up for some serious RNG-grinding, this time can still go lower. There are several seconds of execution mistakes, the routes can be optimized by trading risk and time and the RNG was still far from perfect. My sum of best at the time of writing is 11:17.