My trip is starting to take shape, but I'd like to ask for advice on something...

From London, I need to go to New York on Friday 8 November (I'm locked into this date). Then, I need to be back in London by the night of Sunday 10 November to pick up a flight to HKG. I think it's too risky to fly JFK-LHR on the Sunday dayflight, as it's only a 90 minute connection between arriving from JFK and leaving for Asia. So that means taking the JFK-LHR on one of the redeyes on the Saturday night.

After I return from Asia (around Nov 20), I need to go back to New York, and stay there until just after New Year. So, to do the transatlantic sectors as cheaply as possible, I'm thinking of doing the following:

Fri Nov 8: LHR-JFK on Airline 1
Sat Nov 9: JFK-LHR on Airline 2
(Nov 10-20 separate trip to Asia)
Nov 21: LHR-JFK on Airline 2
Jan 2: JFK-LHR on Airline 1

Unfortunately, doing a RTW from London on Nov 8 (which would mean not having to do one LHR-JFK roundtrip) is not an option.

Is this classic back-to-back ticketing and illegal? Could it be a real problem, even if the 2 roundtrips are on separate airlines? Or, is it impossible for Airlines 1 and 2 to know what I'm doing, and I'll be OK?

All advice welcome!