In that picture there is a circuit breaker between the batteries and the motor, if you knew what it was rated for then you would know what amp range we are actually talking about here.
You probably could take an r/c controller and swap out to higher voltage mosfets and just add enough of them to handle double the current you expect to see and I bet it would work pretty well.
Then just add a motor to steer the car and you have a really big r/c car 