SAS is the handling agent of TG in CPH. If the MAN underpaid/overworked checkin agent doesn't want to interline then you have to do it again in CPH. Once upon a time SAS used to allow checkin the day/evening before, maybe they still have it in CPH, it wouldn't hurt to ask.

There is no restriction on checking thru bags on an overnight connection. The bags stay parked in the system and await the loading for the flight next day.