Thanks all for this informative thread.
Next week I'm taking QF9 PER-LHR booked through Qantas Business Essentials (anyone else use them?) then catching BA LHR-ABZ booked direct with BA website. That route is still listed by Qantas as a codeshare so I'm hopeful I can interline bags.
Otherwise I have 3h to collect T3 and bag drop T5. Should be do-able but much more convenient if I can check bag through from PER.