I think I have come up with a creative way to address this problem:
JFK-LHR (Ticket 1 - UA Ticket, UA Metal)
LHR-FRA (Ticket 2 - LH Ticket, LH Metal) connecting to FRA-JFK (Ticket 2 - LH Ticket, UA Metal)
JFK-FRA (Ticket 2 - LH Ticket, UA Metal) connecting to FRA-LHR (Ticket 2 - LH Ticket, LH Metal)
LHR-JFK (Ticket 1 - UA Ticket, UA Metal)
I can even use my UA SWUs to upgrade the FRA-JFK legs.
Am I in the clear here, avoiding any potential back-to-back problems with UA?