CeeFo - A 5v regulator would work, but its probably not going to sound quite right.
Witchfinder - I'm assuming that if you know tjat the conditioning circuit is giving you the right length triggers, then you've looked at them on a scope? If so, what are you actually seeing for the hat trigger at TRIG_IN2, when you trigger it from TRIG_IN1
The the noise for the top end of the snare working properly?
It seems unlikely that the LM324 might be damaged, but i guess its possible. Have you checked D4?
If the trigger and noise part of the snare are ok., then i'd probably be looking at the transistors in the hat at T6 and T7, unless you have something shorted somewhere