Keep in mind a few things, you bought a ticket to MIA, if there is an issue along the way you could be rerouted to MIA in a way that you don’t go thru JFK, skipping the last segment is actually against the rules, you aren’t too likely to get caught but if you do there are penalties, you have no real protection if you are late and miss your jfk to lax flight, many people would probably book the lax flight on delta to remain under the radar, if you book on aa don’t put in your ff number as that will greatly increase your chances of getting flagged and having the overlapping flight cancelled

in the end the answer is what you are doing is not permitted though often done but it comes with risks that might not be worth 30,000 miles of savings