I have spoken to both BA and SAS about this now, and the conclusion is - never book a mixed alliance ticket with a tight connection.

1. SAS can't guarantuee that they will be able to print a boardingpass for the ARN-LHR flight (which is the one that I absolutely need a preprinted one for, because of the tight connection. Apparently, and this is quite humorous, it works "sometimes" and sometimes not, whenever the IT systems feels like talking to each other (note that this is the official explanation from SAS....!).

2. If I check in online with BA (since the entire UME-ARN-LHR-ORK-ticket is a 125-ticket, SAS can't guarantuee that I will be able to come to the airport and check the luggage all be way to ORK. This can ONLY be guaranteed if I check in at the airport.....

3. BA is showing no interest in helping out. Spoke to a very rude service representative today that explained to me that I would have to come to the check in counter at ARN to get a new boarding pass for ARN-LHR.
Still, I think that they have check in kiosks, so that is a valid option still.

4. The only option right now that looks appealing is to do carry on luggage only and check in online at BA for a complete set of BPs.

Is BA strict on carry on allowance, or can I do my usual "SAS approved" carry on, with slight overweight?