Hi there,
As a UK resident I had a similar issue a few years ago. In the end I went with UA, mainly because they offered miles on even the discounted tickets. My advice, and the reasoning is:

Focus on UA and QF.

As you like to get free flights rather than upgrades, UA has worked really well for me. A round trip LHR - SFO gets (approx) 10,000 base miles and with the Prem. Exec. bonus, it comes to a total of 20,000 miles. This is the amount needed for a roundtrip almost anywhere in Europe on either Lufthansa or Austrian. I think that Thai offer Australian and/or NZ awards for about 100,000 miles.

As you have stuff booked on OneWorld, go for the QF. I stopped flying BA & AA as they wouldn't give miles on the deeply discounted tickets I normally buy.

Hope this limited info is of some help,
Jason