ET is on SABRE so you need a 6-letter PNR (no numbers) to use their Manage Booking tool. I believe SAS is on Amadeus so if you can pull up the SAS PNR in the Checkmytrip app, it will also tell you the linked SABRE PNR. You can view and manage any PNR on the website regardless of origin, but obviously ticketing related functions are inhibited for non-native PNRs.

Not sure why you are having problems reaching the call center though. I have called them literally hundreds of times and never once not been able to get through. I usually use the US toll free number as it is free via most VOIP services. Alternatively, you can message them on social media (I find Twitter/X is the quickest but others also can help) and they can sort out basic stuff that doesn't require payment there like seat assignments, etc..