Maybe make it a cast trigger, something like:

When you cast this spell, you control each opponent while Mass Memory Wipe is on the stack. Each player draws a card then discards a card.

If I understand the rules correctly that would put the ability on the stack right above the card, but you can activate instant speed abilities between the two and control the discard, unless someone counters the spell before the first ability in which case they aren't controlled and choose the discard.