Booked my flights!
Positioning to OTP and then to LA at the end, so in total (LHR) - OTP - LHR - JFK - LAX - PHX - (LAX) - PHX - LAX - JFK - LHR - OTP - (LHR). All in business bar the positioning flights, and got some lovely seats upstairs on the LHR-JFK flights. Cannot wait!