I've been a casual mandolin player almost as long as I've been playing guitar. However, I have always had this problem, and never noticed it until now. When I pick, I rest my hand near the bridge, which obviously leaves little room, and I end up hitting the fretboard on the E and A strings. I tried correcting this by playing with my hand behind the bridge, but I can't palm mute that way, and the open strings end up ringing a little.
I realize that I'm probably not the first player to ever have this problem, and decided to come to some real players for advice.