We have this same problem. At home we have a king size bed and really don't want to sleep in anything smaller. I was told by Disney that we could not have a roll away bed in a room that was just designed for a king bed due to fire code limitations. In other words, we would have to book a king room that also has a sleeper sofa in it. I do not believe you can book a plain king room for 3 persons, just 2.
We ended up renting points from a DVC member for OKW for a studio room. It came out a lot cheaper and at least we have a queen size bed. I do believe, however, that the 1 bedroom units have a king size bed in them. You might try this route.