Just looked at your itinerary again in detail.

1) BNA-LGA-LAX. I am fairly sure that AA does not fly LGA-LAX. Probably you were planning on skipping over to JFK and doing JFK-LAX. However, I discovered to my detriment that a land segment even between co-terminals such as LGA-JFK (or in my case EZE-AEP), counts as a segment. I think this will put you over 20 segments, if I counted correctly. I think AA does have one Eagle flight per day BNA-JFK so that might fix it for you.

2) I don't think CX is currently flying to CMB due to the volatile situation there. If you are trying to do a long leg within Asia, probably your best bet is HKG-DEL as I am doing.

Happy Travels.