Thanks for the mega tips everyone. I guess I'll just stick to this method and work on refining it through practice. Following a specific order of operations is something that helped immensely when I started solving 5x5 and bigger cubes, so it makes sense that I should implement some rules like that for mega as well.
@mafergut I've had a few center caps and screws blast out on my new stickerless ridged dayan as well, and I think I know what the cause is (and a possible solution). I think when the faces are turned counter clockwise the friction is gradually turning the screws as well, effectively loosening them from the core to the point of release. I suspect that if you only ever did clockwise turns they wouldn't pop out... Though, that's no solution

. I think the solution is to lube the core very well. A healthy dose of lube should reduce the friction that is causing those screws to turn. I'm also considering a very tiny strip of plumbing tape to help keep those screws in tight.
I'll definitely post my thoughts on the new Yuxin 6x6 and 4x4 when they get here. I'll do an unboxing if I can resist opening it until late evening when I have time to record. I make no promises