After having gotten my hands on the game, and having seen first hand how silly the grind is for all the custom moves, as much as I really wanted to have them in competitive play, this really kills it. From a mechanical point of view, they offer a lot of new gameplay opportunities to a lot of characters, and can help breath life into a lot of characters that could otherwise be relegated to uncompetitiveness. Sadly, getting them unlocked on enough systems to run any competitive environment would be an absolute logistical nightmare.
Maybe next time they'll put in custom moves available from the get go, but for now, sorry, they're dead.
Play through classic mode and hit the home button during the roulette wheel. I've gotten custom parts on every stage and my best time through classic was receiving 10 custom moves (+ 10 or so other random stuff.) Make sure you pick the Red path, which is the most difficult and gives you better rewards. I think my lowest was three, but I can't remember if losing matches was involved in that.
The worst part is that you can unlock moves that you've already unlocked for some reason. Which means your chances for unlocking certain moves doesn't increase as you play. However, I've noticed that playing a particular character seems to increase your chances at unlocking their moves more than other characters. (If you are playing as Megaman in classic, you'll have a better chance at unlocking megaman moves. This is based on nothing but my feelings, I had collected no data for it.)
I've been unlocking about 5 custom moves per playthrough. So, assuming there are 48 characters with moves to unlock in the game. There's 576 possible custom moves. So, on average you have a 1/115 chance assuming the average 5 moves per classic.
Based on my assumptions and experience thus far:
Assumption 5 moves per classic play through.
Assumption all moves equally likely.
Odds:
Receiving any particular custom move per classic play through: 4.3%
Playthroughs required to obtain all moves:
99.9% = 791
99% = 527
90% = 264
75% = 159
So, given my assumptions, most people could unlock all the custom moves by playing through classic 3-4 times with each character. That is less than 100 hours of gameplay. I'm not seeing how this is a problem.
Edit: I just got my "Unlocked 50 custom moves" message, and I've played classic 11 times.