So what exactly makes "Fast stage 5/10" happen? Is it totally RNG or is it dependent on how you play somehow?

For stage 5 it's based on the amount of damage you do to ben-k. In the PS2 version, Ben-k's health needs to be lower than 90% after the first attack phase, 65% after the 2nd, and 20% after the 3rd, and 90%/70%/40% respectively in the PSP version.

Don't remember stage 10 as well but it works the same way; you need to get zowie's health down to less than 40% after the second charge phase, and also get zowie's health down low enough after the first, to get the fast stage 10.

Gotcha, thanks.

So from what I can tell from the TAS videos, letting go of long notes a bit earlier charges more HP for U-1 and also does more damage to the bosses, correct?

Is this the strategy to go about doing enough damage? Or is it better/more consistent to just try to follow the notes on the trace line from start to finish?

on the ps2 version imo it's better to let go of the long notes a bit early, especially on stage 5, as you won't deal any damage/gain any health if you release too late. On the psp version, however, you'll still deal full damage/gain full health if you release late.