This project would be far simpler using a body-on-frame vehicle like a compact pickup truck. You would have to keep it low to avoid tip over concerns. I've seen several pickups that have a shortened wheelbase - just cut and weld. Doing the same down the length of the truck is probably only maginally more difficult. The difficulty factor comes in narrowing the drive and suspension systems.
I also like the idea of modding a convertible. Cut off the windshield and cover the rest of the cockpit. Then add a small F1 style windscreen and a fairing behind your head, like those old road racers.
