If you have an extra DKK 600 to spend you could probably just book more expensive flights with better timings or a direct flight. For me it would have defeated the point of the trip to spend that amount, even though on a different trip I might easily pay double that for a hotel.
I think the original poster wanted to fly SAS for mileage earning reasons, and is constrained by there being only one morning flight CPH-ATH. So, unless he/she relaxes the mileage earning constraint, the overnight stay in CPH will remain.