If I were propagating, my first choice would be to get a cutting that has no flowers after leaf out; time-wise, I would get it in late Spring but before the start of the middle of the summer. But, keep an eye on the moisture; if yours rotted as you said, it sounded like they got too much water.

fyi: my second choice would be to get cuttings during winter since mopheads can also be grown from hardwood cuttings taken during winter.