This isn't going to work. Your route LAX-SJU-POS-MIA-LAS-NYC-BGI contains three NA transcons. You are only allowed one.

You could do LAX-LAS-MIA-POS-SJU (or MIA)-NYC-BGI but there is currently no direct flight LAS-MIA so you would be 1 segment over the NA limit. What I would recommend is that instead of buying an extra oneworld segment, you buy a cheap one way on one of the many carriers that fly LAX-LAS. It is almost a commuter flight and these tickets can be advance purchased for about US$50. That way, you can use the segment saved to get from LAS to MIA (or SJU) via DFW or ORD. Depending on when you are traveling, you may find that AA has restored the direct LAS-MIA flight in which case you wouldn't have to do the separate LAX-LAS ticket.