Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
What about flying AA/QR, and crediting to either AA or BA?
It looks like the only way to avoid two connections is to fly PHX-LHR-IKA on BA/IR.
In order to earn any type of elite status on either AA or BA, one must fly at least four segments on that carrier's metal per year (in addition to meeting the other requirements for status).