Maybe just make it so that players can't press space in the places that have a floor right above. As for the boss, maybe make a barrier in front of him. I wouldn't recommend making a cooldown because some of the glitches can be replicated without spamming space, and I feel like a cooldown would make the game a tad less fun.
Also, sorry about the poor video quality; I had to compress the video from 420mb to under 25mb.