I would make sure that you don’t sacrifice your snare sound to get a good tom sound. I would do the opposite since your snare is the main voice of the kit. Get it happening and then try to tweak the two mounted toms until you have a sound you can live with. You won’t get rid of all snare buzz, but you should be able to keep it to a minimum.
I cut down my wires as well, but I know you can buy 12 stands. Makes a big difference, that‘s for sure!I had a 20 wire on there. I cut 4 off each side this morning and cannot believe the difference. Did you cut a wire set down or but 12 strand concert tom wires?
It happens, but there are levels that are aceptable, and levels that are not.Sympathetic buzz happens, don't let it ruin your snare sound.
Always change the way you tune the rest of your kit first.