what trans to use for road race?

Don't listen to the lose the bb and go sb... the weight diff isn't 500 lbs between the sb and bb...more like 100lbs

If you want to be serious and competitive your aren't going to put the motor in as per factory anyway, you'll want to center it in the car, which it isn't now.
move it back and down, and level it, not have it on any of it's factory set up..use a shorter custom oil pan.

I ran my car with a b motor, auto and gv set up, a&a did my trans specifically for road racing, cornering and pulling away and embarrassing super expensive sports cars were never a problem.

What class was allowed for engine movement? Any pics of the car?