I'm no electronics expert, but I had a gentleman from California (actually, an ex-employee of Stars Guitars) put together a transformer box that allows me to take mics down to instrument level and vice versa (XLR on one side, 1/4 on the other). I think this takes care of the impedance differences, and could solve the problem you're describing.
A search on Google for 'transformer mic line' brings up
this page, which may be some commercial versions of what I've got.
Again, my knowledge of electronics is limited at best, but hopefully this helps.