I have a place near Penn Station and take the LIRR to JFK almost religiously. But the most expensive part of the journey is the Uber to Penn. Having a shuttle that picks me up at my apartment and deposits me in Jamaica would be a solid pitch against the LIRR.
That sounds like the old Super Shuttle (which I know from CA, not NY).
I thought Uber's offering was more like a bus - you meet at the terminal and it takes you to the airport.