The motors are fed directly from the 6V battery and they work fine. I will not change the voltage to the motors, 6V is their max rating.
For the arduino board however, the specs say that the recommended input voltage is 7-12V and that's why I was wondering if it would be a good idea to bump up the voltage supplied to the board.
No point in raising the voltage, just to drop it again for the motors. The Arduino runs fine on 6V. It's not "as efficient" in bringing that down to 5V, but you're also not doing mission critical work here. I wouldn't worry about it.
I would still suggest developing a custom board though. As opposed to either taking that spaghetti of wires and shoving it in some kind of enclosure, or covering the whole thing with some clear epoxy. It's not that hard to do. My offer still stands.