I have done something similar before, but instead of JFK I did HKG-JFK/LGA-JAX etc. instead of doing a lot of walking + waiting/taking the train within JFK...I'd rather just hop on a cab exiting the JFK terminal and in ~15 mins arrive in LGA (assuming good traffic of course). I have done LGA-JFK ~9-10 am / 9-10 pm and JFK-LGA ~1-2 pm...usually not bad.