A double alternator setup would be all custom (obviously) but there is room as long as you're not trying to keep A/C.

The Accent's shifter works fine. It can even work on the Beta transmission if you were swapping.

I don't think there is an underdrive pulley kit available, but there are lightweight pulleys available for the Beta. I don't think you would want underdrive pulleys anyways if you're running a lot of amperage. It would sort of defeat the purpose of installing a second alternator if you can't run anything more than headlights at idle.

Limited slip differentials are somewhat difficult to find. Your best bet is going with a Phantom Grip if you're keeping the Alpha trans. There are better options available for the Beta trans, such as a Quaife LSD.