I use the EMAD system on my 22" Gretsch bass drum. The problem I'm having is the damponing ring (I use the thin one) keeps slipping out from the holding ring. I find it coming out about 20-30 min. into a practice session and have also had it fall out totally during a gig. (...)
... and you just demonstrated why i dont use the EMAD anymore.

but you could try getting some grey insulation foam from your neighborhood hardware store, and stick a few pieces inside to jam the ring against the head. but that only adds more muffling.
OR, best bet is to just switch to an Aquarian Super Kick I. IMHO, they sound similar, tho i think the SK sounds rounder. and you dont have to worry about the permanent felt ring ever falling off.