To me, the complicating factor is the heavy luggage.

If he desired to try to save a few dollars by using Path then Airporter, not only must the luggage be dragged on Path to the corner of 7th and 33rd, the OP must then join the line at JFK to check said bag before going tbrough security and onward.

With those factors in mind, and the other time constraints, I think a direct private vehicle is the only viable alternative.