I've never actually seen the inside of one so the best I could do is make suggestions. By the look of it space to work with would be no problem, you could fit all of the circuitry and batteries in the base. For simplicity's sake, making a battery door on the bottom would be fairly easy; otherwise you're only going to be able to run one battery. I'd recommend having your atty or cart recess into the joystick, it would look much less awkward.
I'd need some idea of how far and how technical you're willing to go with this thing, you could make it simple or make it out-perform just about any commercial mod available. It's up to you. If you can provide inner dimensions that would be incredibly helpful in recommending what hardware to use, but I will say using a pair of 18650's is going to be your best bang to buck option. If a USB charging option is mandatory you'll need to do much more in the way of planning, soldering etc. More info=more help - good luck, I'd love to see it finished...
