Transmission: Ideal would be a direct drive like all other BEVs. Possibly a low and high gear. High for all road driving and most offroad, low for crawling.lots of stuff
Liftoff oversteer: Tesla's are RWD, as well as the Smart cars. It won't be a problem.
Jeep could easily do a single electric motor going to the existing transfercase. Since the wrangler is also used as an overlander, I wouldn't be surprised to see a small gas generator on board to charge the battery pack. This would also allow them to use a smaller battery pack. And a series hybrid would be less complicated than a Prius solution where the gas motor also provides movement.