What you want is an H-Bridge.
I have a writeup on Everything2 about them, but E2's been down for upgrades for a couple weeks. This should be helpful, though:
http://www.dprg.org/tutorials/1998-04a/
You vary the motor speed with the PWM signal from the single direction speed controller, and determine the direction by means of the H-Bridge. (Which is what everyone else is suggesting, just a bunch of switches.) Theoretically, you'll get more resolution for the control of the motor speed, but that doesn't matter much.
Also, if you can't find relays that can handle enough current, you might be able to make your own heavy-duty solenoid relays. Just a thought.