Update from CPH:

The very welcoming check in lady at Athens, albeit being very friendly like all A3 personell in general is, said they can never check baggages through on a flight that is not 0n the same ticket, even not on any other Star Alliance carrier. Perhaps she just didnt know how to do it?

In Brussels however they had zero problems in interlining from SN onto the FI flight at all. The check in lady there did immediately understand my request, looked it up if it was possible, and swiftly managed to print the baggage tag all the way to KEF.