I would go by airbnb.com too but those are mostly not going to be serviced apartments.

There are a fair number of consultants based in CPH who are gone Monday-Thursday/Friday. Some of them living by themselves would probably be game for renting out their place during part of the week. But there too, no service probably.

Is this going to be for just Monday night, Tuesday night and Wednesday night? Perhaps given the volume of room nights, some hotel may be willing to provide 72 room nights for 1000DKK/room night or even something closer to half of that. Or is the cost of meals expected to be lower too than just the cost of accommodation?

There are some serviced apartments in Copenhagen, or at least there were some companies that used to advertise at CPH airport about them. Haven't seen those ads in years however.