Also note that from JFK you'd be taking the E train to Queens Plaza (the E doesn't stop at Queensboro Plaza). The 7 having weekend troubles shouldn't be too much of an issue for the Verve, since it's very close to several other lines at Queens Plaza and Queensboro Plaza.

Have you tried pricelining something in Manhattan for those nights? My parents are currently at the Sheraton NY on a $92/night stay and are very happy with their room. Unless you're really into the Jacuzzi, I'd take a $100 room in Midtown over a $175 room in Long Island City any day.