[Andy A.]

A little clarification-

No, you can't modify the motors and still compete with them.

Additionally, you can't really fix a fried motor, at least not in the traditional sense. Whats burning is the insulating enamel on the wire coils of the armature. Once that coating is burnt off the wire starts to short against its self, decreasing the effective strength of the magnetic field it can generate. Torque decreases accordingly. The only way to 'fix' the motor is to either rewrap the coils with new wire (nigh impossible to do by hand) or replace the armature. For a small DC motor like this neither option makes any sense.

Mark the fried motor and use it for R&D purposes that don't require full power, or toss it.

You can buy new motors from Lego and Pitsco. $30 each and make sure you get the same part number!