[Overdriven]

Forget about going solid (or in kart terms "live") axle. Number one it requires welding and its out of your budget in parts alone as you'd need the axle, axle hubs, new wheels and tires for those hubs, sproket hub, sproket, brake assembly and weld the flange bearings to the frame.

Wheels. Unless you have a way or someone to pefectly line up the hubs in a new set of wheels I don't recommend drilling. Racing karts use wheel with 3 bolts, maybe the pattern is the same. Either way they can be expensive depending on what you get.

Personally I think you can work with this thing. I'd try and find a 48 volt controller, beg, borrow or steal enough bateries to try it out on 48 volts to see what happens. But I think you can have some fun with it on 48v, if not dump the controller and the kart.