I don't recall numbers, but off the top of my head I recall hearing that Goldwing engines are heavier than you'd think, eating badly into the "lightweight bike engine" thing. OTOH, they are already shaft drive, I believe they have an electric reverse facility, and for a bike engine they're huge displacement.
When it comes to that approach to the bike engine thing, I'm curious about the 2.3 liter (!) triple from the Triumph Rocket III. No reverse, but the other advantages of the Goldwing remain.
Then there's the latest BMW 6-cylinder engines. Transverse, but shaft drive.
I think the simplest answer for a lightweight racer is Hayabusa. It's been done a lot, much is known about handling oil pans and drive setups (you can run in longitudinally with a shaft adapter that replaces or mounts to the output sprocket, or run it transversely with chain drive). I think this is probably the most hp/$, and they'll put up with forced induction to ridiculous power numbers. While they're somewhat less-often used, similar things could probably be said for the giant Kawasaki and Honda uber-sportbikes.
If you have the $$$, go to Quaife and get one of their boxes that more or less mounts to a transverse bike engine and provides a torque sensing diff and a reverse facility. But its a couple thousand dollars, IIRC.
In the end, most of your questions can't be answered by "what's the best powerplant", as they also affect packaging, or get caught up in what you're trying to achieve. Do you need reverse, or is the only place it ever has to maneuver the grid of an autocross? How heavy (i.e. will it be no fun to drive with a peaky engine). I do think you're not going to find something with a good specific output by modern standards that's air cooled, and even if I'm wrong there, getting airflow to it in a car doesn't sound like any fun to me.
EDIT: And of course, this is all the stew in my head after a bunch of reading. Take it with salt, I've never built a bike-engined car.