[TAPKAE]

"I was really happy with the sound of everything except the snare top, and that may just be that the snare drum itself had a kind of hollow, ringing sound. Maybe it was tuned a little tight? However, the underside got a nice crack to it from the snare. And the overheads seemed to do alright on their own."

That's why I say, the 3 mics are what you need to carry the drum sound. In my case, I rely on the overheads alone to be the snare mic and the "compressor" of the the entire kit. I do use the other 4 mics I put up, but all the tone and balance is carried by the overheads. The kick mic is there to fill in the bottom. My overhead snare sound is as good as I could want, and significantly more appealing than the close up mic which doesn't hear the drum the way a listener does. Even a bad room and some mics that aren't crammed onto the drums can be better for micing with overheads. I have a far from ideal drywall box of a room that somehow works out well enough, and the overheads are the heroes of the drum mix.