My earlier post is a fairly good solution. The 1" glide used for furmiture
will help overtones- but all artifical drums will not be as warm
as wood. Tuning reduction and durability can often outweigh this.
bottom of head 1"-2 " in- work well.
One thing I have done to tame a ringy drum was to thumbtack a tiny tuft of nylon stuffing (like in a stuffed toy) inside right where the bowl joins the tube. Too much will really deaden your drum, a little bit, or really little bit ( it's surprising how little it takes) should tame things. Good luck.