Yeah, starting in OSL, whilst saving a good amount of £ over LHR, does give you some limitations as does including EDI within the ticket.

I think I’d go HND to LHR (self return to EDI) and save a flight (3 now) for the mini trip starting at LHR, which would give you more options effectively, as a return trip out of LHR, remembering you can’t have another stop over so you’d need to book a connection of less than 24 hours from LHR to OSL even if not flying it, to complete the RTW.

Say book LHR>Wherever in E/ME>LHR>OSL and maybe don’t fly the last leg.

You will get TPs and Avios on both AY and QR with your BAEC number on the booking, but they’d only count against the 4 flights if they are booked as BA codeshares.