[Andy4639]

There isn't any real way to make it faster other than adding another battery in series. Which would mean it would be 24 volts instead of 12 volts. Which means your charger want charge it also. You would have to get either a 24 v charger are use 2 12 v chargers. If you add another battery in parallel it will only run longer but not faster. I assume it has resister coils setup. If so you can add the 12 volt in series and it should about double the speed but how long it last is any bodies guess per the coils getting twice as hot.
You don't have a bunch of room either for the battery. Those things where made to carry real heavy loads and not for speed. Which I'm sure you already know this. Some pictures of the wiring would be nice it a pretty straight forward design though.
You may could put a little bigger tire on it but then it would take away some of the torque. I don't think it would speed it up that much though on 12 volts. You could possibly take the motor out and see if you can get it rebuilt by Plum Quick Robby & Matt to help it out some. Are Vic Dejohn D&D motors.

I took this cart which is a resistor cart 36 volts and made it 48 volts. Added the bigger rear wheels and a high speed motor. It runs 35MPH now.