MC-engine cars have gotten more sophisticated than the Berkley or the Morgan 3-wheeler. Consider this:
http://www.racingconcepts.info/rs/
The Speads RS11 can run a number of MC engines. The one pictured, #8, is driven by my orthopedic surgeon, Dr. Kirk Kindsfater, who has done quite well. His has a Suzuki R-1 engine I think. The track is High Plains Raceway, east of Byers,CO on US-36. They have track days,
but, you've got to wear leather, you can't have antifreeze in your engine, everything has to be safety-wired. I'd love to try a track day, but I'm not going to buy a leather suit for my body, and I'm not going to change coolant.