So other than the obvious, "proper tuning" answer;
I was wondering if anyone had any techniques for reducing ring in the snare from the toms being hit.
Tuning the drums has got it most of the way there, and the ring is tolerable.
Just looking to improve,
Good drummers often seem to have damping rings or strategically positioned bits of tape on their snare heads.
But be sure this is a real problem. Do you hear it when listening to the whole kit, the whole band even? Or just when getting over-analytical on individual tracks?
You don't have to write songs. The world doesn't want you to write songs. It would probably prefer it if you didn't. So write songs if you want to. Otherwise, dont. Go fishing instead.