Thanks for the quick replies.
In my OP, I forgot to mention that the reason I'm not flying directly in the first place is that I'm only allowed one trans-continential flight, (CX889 JFK-YVR is my first). I'm obliged, then, to travel LAX-MIA/FLL with a connection. LAX-SJO-MIA was, as noted above, nearly as long as LAX-BOS-MIA. However, LAX-BOS is out because of the mono-transcon rule.
Are there any other central american destinations (as far south as PTY) that I can fly on AA metal between the two cities? I suppose I could fly into PBI as well, though I don't really think it will help much.
Thanks again for your help.