I sent you a PM with a link to the apartment we rented. Our daughter wanted us to stay near the metro line since she was coming in from Lyngby. The location ended up being perfect for its proximity to food markets, metro, attractions, and shopping areas.
We encountered the same issue you are with the 3rd person in a hotel room. Because restaurants are very expensive in Copenhagen ($100 a person), we knew we had to do a lot of our own cooking. Having a kitchen made our trip so much more convenient. Full disclosure, I hate to cook, and hubby loves to choose exquisite restaurants when we travel, so staying in was a different experience for us. But it ended up being lots of fun, because the food at the market was exceptional.
There is a thread on CC that discusses best practices when renting through Airbnb. Probably searching for Airbnb will bring it up.
I’m glad you’re considering going this avenue.