I really think that a Fuzz Face will sort you out, but maybe not a stock one. The Fulltone 69 is a nice Fuzz Face variant that allows you to dial out all that nasty, farty bottom end.
My own Big Beard pedal takes my own variations on a FF and gives you the option of that farty bass, or a much tighter response via the tone control. I'll have to put up a demo of that pedal, its a really cool one if you're into fuzzes.