Thermal protection is nice to keep you out of a problem, but they are almost certainly more protective than you need.
20 Amps is a little higher than what I'd like to see for continous use, but it is not outrageous. My rule of thumb is to load the motors to 1/4 the stall load, you are running at 1/3.
I think you will be okay by switching to the non-thermal protected motors.
But then again, I am a run 'em as hot as you like, just don't burn 'em up kind of a guy.
FYI, teams I am associated with typically buy
Freeze-It by the case ;-)
Joe J