Thanks Jerry for the help, especially pointing out the problem with

A friend has advised me to fly LHR-LAX and then back track across the US to maximise the time in F. So I'm not sure whether LHR-JFK then onwards is better or not?

My personal aims are:

(1) Try a variety of top airlines in F including BA, AA, CX and QF.
(2) Maximise tier points on BAEC rather than miles per se. So must maximise the number of segments over 2,000 miles in F.
(3) Do so as cheaply as possible so to start at at cheap starting point.

Will do a bit more research online.