How about an old Nissan 200SX? The first few years had a solid rear axle. The later models had a VG30 engine, so there should be more than enough room for pretty much any 4 cylinder. A Nissan SR20 is probably not a difficult swap, and is pretty darned stout. Weighs around 2600 lbs stock, and has a long enough wheelbase that it might not be a total handful on a dragstrip.
Have no idea how much tire can be fitted under it, though.
