If connecting to QR, your best bet is going to be AA.

They won't interline or protect your connection (they stopped doing interlines on separate PNRs even though both are OneWorld) but both QR and AA use T8 at JFK so it should be fairly seamless to get your bag and then walk upstairs to the check-in counters and re-check for the QR flight.

If you fly Delta you'll have to make your way from either T2 or T4 (depending where you flight arrives) over to T8 which is going to take a lot longer than simply going up the escalator as is the case for AA/QR.

Sounds like you already decided on JFK which is the better choice since QR goes out of T5 at ORD which is a pain whether flying DL, UA, or AA for the domestic flight.