Just finished my first study of some of the top runs (particularly Mike's 30:34 run, since that one uses the DOS version). Here are some things that I'm not sure are known. It's obvious that both former and current top runners have put a lot of effort into optimizing this run, so it's no surprise that I didn't find many things and most of them are not that useful.

In chronological order:

1. It's easier to use the swamp with the bucket if you position the cursor on the bottom right area of the swamp's hitbox. See the using the swamp with the bucket video for an example.
2. It's possible to get from the swamp to Woodtick in 2.4 seconds (it usually takes between 2.7 and 3.1 seconds). Getting the right path is very hard, though. The idea is similar to what you do to get from the mansion on Phatt Island to the waterfall in 5.4 seconds, and I use the same strategy: try to start with a perfect diagonal, and then hope for best while holding Guybrush's hand. My luckiest attempt appears in the from the swamp to Woodtick video.
3. (Seeded runs only) With the currently known best seed (44668882), if you save right before entering Woodtick after getting the string, the rat will start moving after 5 seconds. That means you'll have enough time to use the cheese squigglies and the string, which is faster because you can buffer the second action while Guybrush is walking. You have to save at the right moment, but it isn't a frame-perfect trick. The rat RNG manip video shows one of the possible frames where this works.
4. An easy way to get to the cemetery in 6.1 seconds is holding Enter on the bottom part of the path's hitbox when leaving Woodtick. Then, click on the cemetery once Guybrush reaches the coast. This is useful when going to the crypt in part 2, as the going from Woodtick to the cemetery video shows.
5. Mixing the yellow and blue drinks after getting the hankie from Stan but before picking up the crypt key results in a nice inventory during part 3. You can see the inventory in the drinking at the torture chamber video.
6. An alternative route on Booty Island (which might be slower than the standard route), based on a route designed by SantaClaus, is: get the dress, leave to the map, go to the mansion, get the oar and the fish, use the green drink right before leaving the mansion, enter Ville de la Booty from the left, use the horn, move Guybrush to the flags during the horn animation, pick up the flags, move to the fault line during the animation, wait for the wind, spit, go to Stan's, go to the shop. The spit slide route video shows this route.
7. (Seeded runs only) With the currently known best seed (44668882), if you save before entering the spit contest, there's a good chance you'll get instant wind. I'm not really sure how it goes, but my guess is that about 50% of the frames after Guybrush reaches the right side of the window will give you instand wind. The other 50% of the time you'll get a not-good-but-not-too-bad wind, so totally worth going for it in my opinion. In the wind RNG manip video you can see an example of instant wind.
8. The Booty Island mansion is a very unusual hotspot, since Guybrush will still take a different path depending on where you click on. But that means you can use schmoovement by holding Enter and moving the cursor inside the mansion hotspot! The Booty Island mansion schmoovement video shows one possible (probably unoptimized) way to do so.
9. (FM Towns only) After exiting the mansion on Booty Island, click on the light green pixel in the dark green area near the big tree. Then click on the big tree when Guybrush gets there. This saves about 0.5 seconds. The from the mansion to the big tree video shows the right pixel to click on.
10. (DOS/Amiga only) Exiting the cliff by clicking on the top-left corner saves about 0.8 seconds because Guybrush will stop as soon as he hits the rocks on the left, as shown in the exiting the cliff video.
11. (DOS/Amiga/Special Edition only) When going from the cliff to the big tree, clicking on the exact pixel right at the beginning saves a few frames because Guybrush will take a perfect diagonal. An easier timesave comes later, when Guybrush is reaching the woods (are they really woods?) next to the rock. First clicking below the woods and then on top of them makes Guybrush take a quick diagonal. The from the cliff to the big tree video uses these two diagonals to save about 0.7 seconds.
12. (Seeded runs only) Not sure about how consistent it is but, after saving and reloading at the big tree, you could read the disasters book and might always get the same coordinates. That way you'd know in advance where to position the cursor during your conversation with Kate. Of course, this would mean you'd have to do one more task during the tree climb, which is already one of the hardest moments of the run.
13. Here's a not-as-hard way to quickly go from Woodtick to the swamp. Start by taking a perfect diagonal, and then click on the swamp. The timing is a bit tricky, but I don't think it's frame perfect. The from Woodtick to the swamp video gets there in 2.9 seconds with only two clicks. That's as fast as doing a perfect diagonal, but easier.
14. To (kind of) easily get from the cemetery to the beach in 6.6 seconds (matching Mike's TAS), exit the cemetery while holding Enter with the cursor near the top-left corner. Then click on Woodtick or Dread's ship (or somewhere around that area), and then click on the beach. Not sure about the timing, but it seems you have plenty of margin of error. The from the cemetery to the beach video shows the process.
15. Mike's approach starting part 4 is very interesting, using the crowbar with the barrel first; for instance, it makes it so much easier to click on the ocean's hitbox. To prepare the cursor, during the cutscene at the end of part 3, you can switch to another program's window (where you will see the mouse cursor), position the cursor where the crowbar will be, and switch back to the game's window. Then you can hold Enter at the start of part 4 and Guybrush will start walking the crowbar immediately. Or, if you prefer (slower, but more reliable), press "U", click on the crowbar, and then click on the barrel instead of holding Enter. Or, if you prefer using the martini glass first, you can position the cursor there during the cutscene. In any case, you can check the positioning the cursor at the end of part 3 video.

Forgot about the "Pick up bone, "Walk to Walt", "Use Walt with bone" sequence, which is theoretically faster, but very tricky because then you don't have much time to position the cursor where the small key will be. I've edited the post.

Oh, I see that the TAS actually does that sequence :D. Deleted.

For Dinky Island beach, I need to mention that the weird martini glass glitch simply doesn't exist on the German version. But I'm also more comfortable with using the crowbar first.

Oh, that explains why you pick up the glass without explicitly picking it up... I was wondering about that, thanks! :)

By the way, since we're at it, the other thing I'm wondering about your runs is that, when you enter the cliff, you use the fishing pole and skip the cutscene in 3.1 seconds (until the verb changes to "Walk To"). I've tried dozens of times, but I never get there faster than 3.3. Is there a frame-perfect trick or something?

Not sure. I only remember that timing the inputs manually worked better for me on that screen than holding down any buttons or mashing.

I also used to think that getting the "Dang." on this screen saves 1 frame over getting it on the map screen, but I think that might just be wrong.

I still need to test it a bit more, but it looks like the best known seed (44668882) can definitely be used to force a 5-second Chester (saving right before entering Woodtick), and there's a chance it could be used to get instant wind (saving right before entering the spit contest screen).

@mikeSpeedyAdventures By the way, forgot to say that my bet about the cliff is that it might be one of those "German version with DOSBox" VS "English version with ScummVM" differences.

I've updated the post with:

• Rat and wind RNG manipulations in seeded runs.
• Using the Booty Island mansion hotspot for schmoovement.
• A route from the Booty Island mansion to the big tree that saves about 0.5 seconds.
• A route from the cliff to the big tree that saves up to 0.7 seconds.
• An alternative path from Woodtick to the swamp that loses 0.1 seconds compared to the TAS but is not as hard.

Edited the post to include a super-tricky path to get from the swamp to Woodtick.

I'm not sure whether it's already known or not, but just in case, I've edited the post with a video showing a (very inconsistent, except for the first diagonal) path from the Phatt Island mansion to the waterfall.

I've updated the "from Woodtick to the swamp" video. Turns out, it's possible to get there in 2.9 seconds with just two clicks.

I've updated the post with a possible way to always get the same coordinates from the disasters book in seeded runs. Not sure how consistent or practical it is, though.