We have a sleeper sofa with the air bed too, and it's fine for a night or two with adults, but not the greatest for a week or more. It's much better with the 2" topper we keep tightly rolled in the storage drawer. Nonetheless, I don't think it will suit your needs no matter how you "doctor" it, and say you should proceed with your plan B of getting a replacement. If your rig can handle the weight and you can get it in through the door, a bonafide residential sleeper sofa is hard to beat. Otherwise, I think a flip-fold couch with a foam topper will give you more comfort over that time period along with a quiet setup and quick breakdown.
Happy Camping!