Not all sleep sofas have a "bar in your back". My very first apartment was a tiny studio and I bought a full size sleep sofa from the Ethan Allen clearance center to use in it. The mattress was an inner spring and it had a trampoline style suspension under it - springs and elastic webbing, no bars. Despite the name "trampoline" the bed was not at all bouncy
I slept on it just fine for 5 years before moving to a one bedroom apt. I have severe scoliosis and the bed never bothered my back.
The futon is another good option but with anything you plan to sleep on, you don't want to play it cheap.