Yikes! This is a very demanding load on your batteries. To my experience, this is hardly an application where any type of standard power supply circuit can do better than a direct connection between the motor and the battery. The current peaks are very high for such a low-voltage application. Any loss in efficiency of a circuit will be taken off from the power available in the batteries. Increasing the voltage output will also require a proportionally higher current from the batteries.
The battery capacity to sustain these currents is probably the main point where you have to optimize things. Another thing is to reduce the voltage losses wherever you can. At peaks of 50 amps at 7 volts, things like contact resistance at switches and connectors, the gauge of the wires running from the battery up to the motor, and the internal series resistance of the battery will have an impact on the peak power that the motor can generate at a start. (the same parameters as those for a car starter vs the lead-acid battery, the wirings and the solenoid contact).
SC batteries at 3300mAH are good ones. I don't know how quickly they degrade over time, but they sure do quickly in applications like yours. What degrades is the internal series resistance, which has the greatest impact on the peak curent output. I'm sure that you see a difference when you use fresh batteries.
Have you ever measured the voltage at the motor terminals when it is generating high torques as in a start? It is not an easy task with such a moving target, but I'd be curious to know how much voltage remains. A circuit to regenerate a higher voltage would have to work from that remaining voltage, which is surely much lower than 7.2 volts.
So personally I don't think that there would be an easy solution to boost the output of the motor, unless you are sure that the batteries are powerful enough to sustain that increase in power delivery.
Is there room for bigger batteries in the car? like 4/3A or D? Not for a race but as a test. This could show quickly if the peak capacity of the battery is the limiting factor to the car's performance. A bigger battery would normally have a lower internal resistance thus allow for higher peaks.
That's about all I can give as input. Good luck!