After listening again, I think the snare is just too loud in relation to the rest of the kit. First, keep the bass drum in the center of the mix, this will give it more presence. I think the bass drum could also use some eq to tighten it up. I like to use one overhead condensor, and placing it over the middle is pretty effective, you need to boost its volume in your mix, the cymbals are just a little too quiet. The snare needs a little eq, try bringing out some highs, give it more of a crack. The ringing overtones are fine, you might try dampening them with a folded paper towel taped to the head. I think the ringing suits the music, just coming on a little strong. I'm not sure what type of eq you are using so its hard to tell you specifics....but hopefully you can get the general idea