We just flew BNE-ADL-DOH-CPH on QF and QR, separate tickets (BNE-ADL in Y, ADL-DOH-CPH in C).

I asked Qantas premium check-in to check the bags all the way to CPH, and she was a bit confused as they were different PNR's. She mentioned first airline being responsible etc. etc. and had to go and ask a supervisor. She came back and said that they'd do an exception for us and check them through to CPH.

We had a third PNR for CPH-HEL but I didn't want to push too much

Getting interlined checked baggage has never worked for us with AY despite all being Oneworld flights.

Funny thing happened with SQ a few years ago. We were flying NRT-LAX (C) and check-in asked if we had any connections from LAX. She was happy to interline our luggage to DFW on AA -- but US is a bit different as there's no proper transit and you need to take a look at your luggage anyway.