Take that tape/dampeing off the snare. Let it ring a little. Its way too dull sounding. Tune it naked, then add a bit of moonjell if you want to kill some bad resonance.
Read up on phase. Figure out how to adjust your phase properly.
If i dont know how a certain setup will be in regards to phase issues, i usually record all the mics normally, then solo them against each other to determine what needs to be fixed. I start with the kick and overheads. I look at the kick wave form in my daw to see if I am getting a positive wave (wave starts goign up) on the first transient. If thats correct then I leave that alone, and then solo it against the overheads. If the bass gets less full I switch the overheads phase to see if I get the proper bass response.. Then I solo the overheads against the snare and switch phase if I need to. Then the toms and so on. This works for me.
As for snare reverb. I do a similar type of music. When trying to get a good smooth lively snare sound I have found that all the snare reverb in the world never seems to sound better than sticking a mic 4-6ft in front of the drumset, compressed and slipped back under the mix just a bit so you get the resonance of the room. It adds a lot of life and realism to the mix can reveal a nice crack from the drum, and gets you sound that one could think is a bit of verb. This works even on a crappy sounding room.
-josh