I have found a following gearbox + motor combination that fits the rpm and torque requirements needed. They are here:
The motor has a stall current of 85 amps. I am struggling to find a DC Motor Controller that can handle 85 amps at 12 volts running through it. This controller would have to be able to take in 0-5 logical volts to control motor speed, be able to have a 12v input from the battery to power the motors, and a terminal that outputs 0-12 volts proportional to the inputted 0-5 logical volts. It would have to be able to have at least 85 amps drawn through it (probably a little more than that for safety). Do you know of a place online where we can find such a device for less than $100? The highest we have found was one for about $60 dollars each (one per motor) and could only handle a constant 60 amps of current and a peak current of 100 amps for only up to 2 seconds. Because 85 amps is the stall current of the motors, this is unsafe as, if the motors were jammed up by something for more than 2 seconds, for instance, the controllers would burn out.
If we calculate that we need x torque to speed up to y rpm in the necessary time period, buying a motor with x rated torque and y rated rpm should be sufficient, as the torque below the rated rpm is greater than the rated torque on DC motors. Is this correct?
Edit: One idea is to have current limiting. Something to see that when the current could get over 50 amps or so, it would stay at or below 50 amps. What type of circuit could I buy/make to do this?