If you have a metal trap, why the mulch at all? Just to be quiet?Since you DO have a metal trap, then 3" of mulch will be fine, since it isn't necessary to begin with, except to quiet it down. Let me know if I misunderstood.
I have experimented with the thickness of the mulch bed because my first trap was just too darn heavy. And it gets heavier of course as it accumulates spent lead. I stopped at 4 1/2 inches which was about half of the thickness I had started with. I will probably test further reduction this summer but we are still waiting for spring here in Western Washington