I have booked 1st class mileage saver to LHR from STL, only rub is I need to fly to LGA first and then find my way to JFK. I am assuming I need will check bags first to LGA then collect my bags and hop a taxi to JFK for the TATL flight. Seems like it should be straight forward. I have 4hrs to make the connection. Anything I am missing? Is there a shuttle service between LGA and JFK?

Is it likely a call to AA would get them to give me a more straightforward routing via ORD or DFW?