Just finding the new updates on this thread now! I admit I didn't read the giant wall of text above, so some of this might be repeat info. I'll just chime in on a few things that might be relevant to the TAS.
1. Autoscroller skip. As Omnigamer mentioned, we tested this awhile ago, and not only did we find that it wasn't really possible, but if you did managed to land cleanly on the bottom raft, the boss wouldn't spawn. I was trying to approach it with a damage boost (lure a mimic ghost into a really shallow downward angle, then maximize your double jump and damage boost afterwards) but was unsuccessful. Omnigamer made an infinite double jump code to test after the fact. I really doubt it is possible to land on there through any means, unfortunately.
2. The bee transformation is really special because Arthur has no hitbox on the ground. He also gets a pretty substantial boost if transforming in mid-air, which might be useful in reaching platforms that are normally out of reach. It is possible to land on the first platform of 2a with a bee transformation boost off the first chest magician, but I remember it not being faster because bees can't climb ladders. You can also take advantage of the bee special effect to skip the 2nd row of lava in stage 3 without damage boosting (
https://www.youtube.com/watch?v=u3q5lilJO4M). This is slower in real time, so it is almost definitely useless for a TAS.
3. Awhile ago, I tried skipping rotation cycles in stage 4 by damage boosting to the end of 4a. While it is possible to reach the "end" of the screen early, there is no loading zone present.
4. I've been considering redoing this TAS for about 4 years, but there are a lot of things stopping me. This game has a TON of lag and there are some really, really rare occurrences that have the potential to save a lot of time on that front, but I have no idea what controls them. For example, I despawned the background music in stage 2 a few times (example:
https://www.youtube.com/watch?v=dcFHu5u_sd4), but have been unable to consistently replicate it. Sometimes no bats ever spawn in stage 3b, and sometimes no shield guys ever spawn in the ice cave of stage 5. There are so many small things like these that would save appreciable time in a TAS but are so wildly random that I can't reproduce them. I found one way to eventually despawn the bats in 3b by the 2nd tower, and one way to force the shield guys to never spawn in stage 5 with the axe magic, but I can't trigger them in any other way with any kind of consistency.
5. I believe a TAS of this should be two loops, and should use as many different weapons as possible. I think the end result would be an absolutely incredible TAS, but the amount of upfront work I'd have to put in to testing all the different speeds of the weapons is really daunting. I know for the fact that the dagger is not the fastest in all situations, but has really good lag reduction properties. Optimal torch play (like in a TAS) should be faster on every boss except stage 4, and that boss is fastest with upgraded axe. The bosses are relatively simple though; the tricky part is minimizing lag in the stages themselves and figuring out those 1 in a million situations where enemies never spawn or the music goes away.
I know I'm forgetting a lot of stuff, but I can't remember what else I wanted to mention. I post here again if I can think of it.