M4573R:
I'm looking into the feasibility of running 4 high-powered motors on a single Arduino board and am not sure if this is possible with existing shields.
You might be able to do it with four of these:
To handle the motor you are selecting, you would need to run each board in "parallel/bridged" mode so it could handle your worst-case current levels (stalled @ 22 amps). The boards themselves have current feedback, and re-mappable pins - you might have to review that further to make sure that they can still be stacked (otherwise, you would need to keep them off-board the arduino, and run jumpers for the signals).
In fact, it is likely that at your current levels you will not want them set up as shields - read the information on the site carefully and thoroughly - it notes that in order to reach the higher current levels, you will need to directly solder the wires to the motors (as the terminal blocks are only rated up to 16 amps), and that you will likely need to install heatsinks (along with active cooling) - all of which would likely preclude the use of the boards as shields.