I actually have not tried different head combos -didn't even occur to me...Brilliant!!
What head combos have you tried? What didn't you like about each? Perhaps we can glean more from this.
Good questions already raised, & most valid areas for research, but I'll deal directly with the bearing edge issue in isolation.Have you tried everything else? You mentioned heads and muffling, but what about different beaters, front head, and port hole modifications. Also are you talking about the sound from the driver's seat, out front, or mic'd?
Have you read the Drum Tuning Bible (google it)? It describes the effects of a lot of these options, plus has tips for achieving different sounds.