When you start using more than three microphones (Bass Drum [what is this 'kick" of which you speak?], Snare and "Rest" or "Other"), you may well improve your sound, but the chances are better than even that you will make it worse.
Well, more than one mic, perhaps.
Anyway, every little placement change, every EQ change, every pattern change, everything you do to any one mic, becomes a chance for a problem in relation to any of the other mics.
First, try just bringing up your BD, Snare top, and OH's in your mix. For now, eliminate everything else. Does it sound more focused? Are there enough toms? Are the cymbals still washy, or "phasey" sounding? Many great recordings have been mixed with only these mics. If your overheads are not washy, and do have enough toms, then you may have it. If the OH's aren't so great, you need to improve your mic technique for acquiring overhead or room sounds.
Have you tried any stereo placement techniques, especially X/Y? If not, do so.
Anyway, this is just a start. Mainly, keep it simple. Add only when necessary, not "just because we've got it."
Good luck.