I somehow ended up on the Steel Guitar Forum. There are musicians there who wrote that they were playing Western Swing at CW places in the Los Angeles area in the 60s and beyond. Yes, it seems that it was still popular at places like the Green Lantern, Elks clubs, etc. "We played a lot of Western Swing which was still popular." They list a whole bunch of places I've never heard of. If you've been to an Elks (Skippy Blair's first studio was right beside the one in Downey), or if you know someone who has, you might know that it is in general an older, pretty conservative crowd.