So I'm looking to fly from LHR to JFK in February and I'm trying to figure out which combination of fares/booking websites is best for getting both checked bags (less important) and seat selection (very important - especially bulkhead/exit row/MCE) when trying to book a HBO/BE fare while minimising cost.
Outbound: Only option is a late evening AA flight - bookable through either BA or AA. Main Cabin is +£40 over BE/HBO.
Inbound: Choice of either a BA or AA flight (20 mins apart) - either bookable through either place. Main Cabin and WT are both +£40 over BE/HBO

If I understand this correctly, I have a few options each with implications:

• Booking AA/AA through AA - this gets me checked baggage but no seat selection
• Booking AA/BA through AA - this gets me checked baggage but no seat selection on first flight
• Booking AA/AA through BA - I believe this should get me both checked bags and MCE seat selection? Is my understanding of this correct?
• Booking AA/BA through BA - this gets me checked baggage on first flight and seat selection on both flights?

Just trying to figure out if my understanding of this is correct - if so the AA/AA through BA is a no-brainer. If not, I'll need to figure out which flight I need to pay the +£40 to get MCE/bulkhead seat selection.

Thanks!