I think I've optimized Rustic Ruin Act 3. Below 11 seconds seems like it's impossible; probably at this point we're going to fight over frames. In which case, between the lag frames, it's, uh, well, that's frames 77780 to 78446 anyway. I'm not sure if the number I want here precisely for counting it. (Both those endpoints are valid input frames; on either side it's lag frames.)
https://youtu.be/UsdW5NnOVPI
I also think this game may be possible to do in segments and assemble together. I mean like, one player could do one stage, another could do another stage, and we could just copy and paste the frame inputs. (Edit: I fail at communicating well - I'm trying to say, I think single acts are independent of one another and self-consistent, so if we each took an act we could put them together at the end and it would work fine. RAM seems to be non-issue. This is what I plan to toy with and examine.)
I plan to test this... after I get done with my test run. It should give me the level select, I could create a save state, and then it would be - theoretically - possible to test copying and pasting runs together to see what happens.
---
Some notes and observations:
When you bounce off Robotnik, you bounce in the direction opposite the one you try to move... while still facing the same direction. Doing this (instead of holding left to get over) saves some problems and lets us jump immediately as we land, as we're already facing him again.
That hitbump method happens in the world record time. I've in fact tied it for the ingame end-of-stage timer.
You can jump just before you land and it will register the button press. This pretty much has to be the soonest you could press jump.
This run is probably human impossible; there's a ridiculous amount of single frame input in it.
The spindash at the end is just for the hell of it; there's nothing going on there anyway.
---
26 December edit:
So I did do some basic testing with copying and pasting input for stage runs.
First, I ran the entire game. Then I input the level select code. I messed around in there for a bit, playing all of Knuckles' stages and some of Tails'. Then I ran Green Grove Act 2 from there, manually. Then I pasted the inputs I had for Green Grove Act 3 at its start.
Lo and behold, Green Grove Act 3 syncs!
I don't know how far this would work, or what stages would struggle, but the next thing I plan to do is try replacing singular stages and see if the rest of the game still syncs. So it would theoretically only affect the stages after the replacement.
If I can get this working entirely, I'd like to have an open collaboration where people just do singular stages. Hopefully this would lead to this game finally seeing a quality TAS.