If you skip the jfk to lax segment your return will be cancelled, skip lagging is more about not flying the final segment, since we can’t see your fare rules none if us can give you much more advice than you need to call, now if all your segments are on aa and your are very careful you can try changing the segment on line to get some idea of the price, I would be very careful with this and not actually complete the change, my own experience in situations such as yours is that the answer is never what I expected sometimes it is less sometimes more but always vastly different than I might have thought,

you can wait to see if there is an issue with either the fco to jfk flight or jfk to lax which in this case would help you out