This game is a brain melter, and my brain is now mush.
The game uses progression to introduce new mechanics to get you used to the multitasking rules. The checkpoints are an essential component to the game, or I would have probably turned it off as soon as I had a failure, deep into the playthrough. Instead, I powered through the AGONY of the final level.
My strat eventually turned into me deliberately taking a hit to make it to the last button. Given what I could see about the map, there was simply no way to get to the red button, but I didn't need that stupid button anyway.
This is a strong contender, and I'll give you full marks for fun. Now, I should probably go lie down, my head hurts.