converting 4 motor RC car, which motor driver is best suited?

I want to convert a New Bright 1/8 scale 4x4 RC truck to an autonomous racer for when my kid is in his Power Wheels (so it playfully races against him). I'm removing the receiver/circuit board (lost the transmitter), so it'll be just the shell, chassis and wheels. Each wheel on the RC has it's own motor and all 4 spin to go forward and backward, but it has no servo for turning, so to turn left the right wheels spin and to turn right the left wheels spin. The OEM battery is 12.8v 500 mAh li-on and I can't find info on it's rated amperage/current, but when hooking up 1 (one) wheel to my bench power supply I noted 230 mA of current with no load and 4500 mA (4.5 A) when holding the wheel so it doesn't spin. I doubt that battery can really discharge at 36C (18,000 mA = 4500 mA x 4 wheels) so I assume this system at stock really pushes like 3 A (3000 mA, 6C - 750 mA max per motor/wheel).

With the info above and considering the Power Wheel goes 5 MPH max and the RC car maybe 8 to 10 MPH max (with stock voltage), do I need to go with a L293D, 2 x L298N or 4 x BTS7960 motor controller board for this project?