If you were up for a challenge you could try FQTV/FQTS splitting - get the agent to add your QR FF in the FQTV field - that’s the programme where miles get credited to. Then add BAEC no. in the FQTS field - that’s the programme providing the status benefits, and that’s what should appear on the BP for lounge benefits etc.
I think the OP is chasing status with QR.