NDFan and everyone else, thanks for that helpful info. It is all good to know. I was aware of the co-terminal rule, but the validator I used showed a LGA-LAX AA flight. Now that I'm looking at real flights on Kayak, I don't see one... so I may indeed need to catch the all-economy flight up to JFK from BNA. Alternatively, it looks like I could go to MIA or BOS (the longest) and then on to LAX.

About the CMB flight, hmmmm, I didn't think about that. I'm not planning to go there for a while (the end of the trip will be in the summer), so I wasn't concerned with the present booking situation. But if that prevents me from including CMB on the itinerary, I may replace it with KHI.