Sounds like you don't need any electronic drums since only the snare drum and cymbals were mentioned as part of the overall problem. Is there something on the snare to cut down ring? If not, consider using a dampening ring or Moongel. A more cost-effective alternative to Moongel can be found in dollar stores. Look for those gel-like décor items that stick to windows. Cut to size to get desired result.
As previously mentioned, thinner (good quality) cymbals are better in a lively space such as your church than thick ones as they take less force to speak. Yes, the Sabian HHX series are thinner and may work for you. Other contenders: Zildjian K Custom, Zildjian A Custom, and Paiste 602. These are not cheap new. With little effort and some patience, peruse your local classifieds for used ones, especially old Zildjian A (Avedis) from the 70s and older.
