I don't have a solution, but I also tried this (with a Prius) and the gearbox swap didn't work. I know the engine swap did and I'm pretty sure the drivetrain swap did too. When I test-drove it, in the pre-race options, it wasn't locked to AT like it usually is, and I selected manual, but when I drove it the car was rather solidly in D, with R as my only other option.
I think it might be to do with electric / hybrid cars. I'm pretty sure people have been putting Hayabusa running gear into go-karts with no issues.