Lauszus:
I would also need some quality cables, connectors, and some basic stuff like that, that can handle the current.
RC model connectors are very compact, pretty cheap and high current - you have to solder them to the ends of wires and heat-shrink a sleeve on, not as simple as crimp connectors but take up less space. If you can afford/find silicone-insulated finely-stranded cable it will be the business (easy to work with because very flexible, can use thinner wire as it tolerates self-heating better).
Lovely little robot by the way 
Your comment about the speed of the motors intrigues me - I would have thought its the "speed" at which a motor can develop torque is the important point, which depends on the motor controller and the back-lash in the gearing more than anything. A delayed response to control input is going to make the control loop much harder to stabilise. Surely the rpm simply limits the speed the robot can go, not the stability?