I'm just wondering if a photo dryer would be faster.
Way back when in school, I was a member of the photo club. We had this thing to dry prints on. It plugged in and the metal parts under the cloth overlay would heat up; you pulled the cloth down over top and used a roller in an up and down fashion to flatten the prints and press them against the metal. They used to dry thoroughly in about two minutes. Stamps being thinner would probably dry faster, and rolling them flat would ensure they wouldn't curl.
I'm pretty sure the thing had a temperature setting on it, so you could probably use the lowest setting, stamps being much thinner than photo prints.
Something to check into, maybe?