It sounds good to me, except:

If a participant doesn't receive their print by day 15 of month 3 in a cycle, they should PM the moderator, who will drop their sender from elgibility for the next cycle and ask for volunteers to send a print to the member who was stiffed.
I think the mod should first contact the delinquent sender and find out if it was sent and when. It could just be a delay. Check first, then drop em if necessary.