Sounds like your frame was designed for long-reach brakes. You can trim the pads, but that will diminish your braking surface (it is already), which may or may not be OK. Another idea is to get a round file (like a chainsaw file) and file the slots in the calipers a bit deeper so that the pads go lower. I've done this myself and don't see a safety issue, though it's arguably not a good idea to modify something as important as your brakes.
The best solution is probably to get a set of long-reach brakes like Shimano R600s. A new set runs about $60 shipped on Ebay.