What brand of snare is your drum?Shell material,heads,ply count,shell thickness,Are your rims die cast or triple flanged 1.6 or 2.3 mm? All have a lot to do with pitch,tone,projection.Detuning 2 lugs works as long as you're not a heavy hitter,because you will break that drum head if you are.Try using a Remo Emperor coated batter side,ambassador snare side and tune the snare side just very slightly lower than your batter head.I f your miking the drums..back off the snare batter head about a couple of inches.That will fatten up the sound and reduce ring that the mice hears also.If you can though..borrow a Supra 6 1/2x14 Ludwig LM 402 or an 7-8 x14 wood shelled snare like an 80's Superstar birch shell drum...talk about fat.
Steve B