This does happen now and then. I've dealt with it a few times seasonally at the shop.
If the caliper is sitting a bit too high and there are no spacers between the frame and caliper there is little you can do to remedy the problem as the hub/rotor assembly is fixed. Perhaps you could remove a bit of the material from the frame...very carefully...and the bottom of the caliper but you better do it correctly or it will be all f'ed up.
You can and should service the brake pads more frequently as well, this way you can use sand paper to level the pad before it becomes a problem...this also will remove gunk and glazing from the pads giving you better braking.
Sounds like you are very heavy handed when braking and perhaps are using one brake more than the other resulting in faster pad wear...if your pads aren't metallic you may be better off with metallic pads as they last longer but if they get gunked up and glazed they become very noisy.
Brake pads are a regular maintenance/service item and most overlook this...have a spare pair ready to go and life will be a bit easier...