The TK boss has pretty dumb RNG, hitting it on the same frame can still produce different results depending on what you were doing before you hit him. That's why you'll notice that I keep jumping around randomly and intentionally take damage. As far as I know there isn't any method to manipulate specifically what comes out of the box...
If it makes sense, this is (roughly) what I do to manipulate the attacks:
Eg. the boss is first vulnerable at frame #528.
1) I create a savestate a few seconds in advance (let's call it savestate 1)
2) I go on to hit the boss at frame #528.
3) If it gives a jack in the box, move on to next hit
4) If not, I load back savestate 1 and start doing other things, like jumping to the other side of the boss and dumping Sonic into the abyss, then go back to hit the boss at frame #528.
5) It gets much harder to manipulate a jack in the box for hit #7, hence I need to create savestates from the moment I deal hit #6, then repeat step 4.
I managed to get the Sunset Hill boss to sync with the exact same input from my any% run, EXCEPT I somehow regained control 28 frames earlier and finished with a time of 33.86 seconds -_- it's almost funny how stupid the RNG works in this game.
I've been stuck at Toy Kingdom 2 for the past few days or so. I managed to sneak past the early moving block at the 8-10sec mark in the any% TAS, and saved well over 150 frames before getting stopped by the final block in the path. If I could somehow save 3 or 4 more frames I most likely would be able to get past the block; but I've tried the best I could to squeeze out some frames and failed terribly. That would mean I would have to make do with a small improvement of <30 frames or so... Edit: it's done, saved about 3 seconds with a completely different route.
About CT3, I know that Kirby used Knuckles+Tails for the stage to pass through a certain part without needing to fly, but I feel that it doesn't make up for the two areas where Sonic can get boost mode (the beginning, and the part with the speed shoes). Either way, Tails definitely has to be the partner, a +Sonic team probably doesn't have as much potential in that stage.
Anyway, here are the timings of the new WIP:
