Hello Geesk.
A couple of friends of mine, speedrunners Mecha and PJ (also known as theSuperSNES) were experimenting today with TMNT3, after seeing your video. They have a history of speedrunning this game and the glitched state bug where you kill one player was interesting to them to see how easy it is to use in human play - and they were streaming, so a lot of other people were watching and offering suggestions too.
Anyway. I'm not sure if you've tried this... but, after you set up the glitched state for one player, they can then do the exact same process to set up the glitched state on the second player - putting BOTH players into the glitched state.
Is this useful? well it looks like with both players in the glitched state, enemies target neither player, (or at least their behaviour is strange.) Additionally, bosses have even less health, and there are multiple missing spawns.
It's difficult to maintain the state with 2 human players, because some enemies and effects still deal damage (and you can accidentally kill each other) - but for a TAS, you might be able to save even more time.
I've made a highlight video, but Twitch has a bit of an issue right now where new highlights aren't viewable - hopefully that'll be fixed soon.
https://www.twitch.tv/videos/384673505