Now that I have a better understanding of your aims, how about this 14-flight itinerary
Salient features:
44,534 mile, 12-flight RTW from OSL to MAN (or any other UK airport to which QR flies)
of which
37,354 miles, 8 flights are on either QR or JL
Plus
6,447 miles, 2 QR flight MAN-DOH-OSL to be taken any time within the ticket's 12-month validity
Plus
According to expertflyer.com QR codeshares on AA's JFK-SFO flights
Off the wall suggestion:
When you are back in the UK, you could change your ticket to a DONE5, and fly
MAN-DOH-CPT-DOH-OSL
15,677 miles, 4 QR flights
Incremental cost would be NOK8226 plus taxes and charges