I don't know how (un)common 20" or 22" Radio King BDs are. I had a set of '41 Radio Kings in 24/16/13 sizes. That 24" kick sounded amazing (especially in the studio) but honestly, I think you can easily get a "punchy" sound from a 20" with proper head selection.
You mention concern that a 22" will be hard to transport. Even if you found a 20", be advised that Radio King drums are heavy. Seriously heavy. The load-in/out, setup/teardown process is already a PITA, but RKs take it to the next level. Especially muscling them in and out of their cases. My BD had clip on spurs, so that was an added wrinkle to setting up quickly (and added stress of keeping up with the wing screws that hold the spurs in place).
But man, there is just something magical about playing those drums that makes it all worthwhile. They sound special. They look special. Just sitting behind the kit makes you want to try and channel Gene Krupa's playing style. They have such a warm/distinct tone. I would not describe the overall kit sound as punchy though. The kit seemed to cut through the mix better when mic'd up, especially when competing against electric guitars, bass, and keys (in a typical rock band setting). For jazz, big band, dixieland, and so forth, they sound killer mic'd or not.
Best of luck in your search and let us know what you come up with!
-murph