For $600, would you consider...
http://www.ikea.com/ca/en/catalog/products/S09874380/
+
http://www.amazon.ca/LucidŽ-LinenSpa...attress+topper
Double check if the dimensions are correct. I'm pretty sure this sofa bed is about same size as a Queen sized mattress. I grabbed a sofa bed (I think this one) from Ikea and slid the Lucid 3" memory foam topper under the cover. Works great as a comfy sofa and a nice bed. There's other mattress toppers that are cheaper, or if memory foam isn't your thing. This was what I did and it was awesome to crash on and it was easy to prop back up when company was around. I regret paying extra to upgrade the mattress. Money was better spent on the mattress topper.
The only slight issue with this set up, is that if you sit on the edge when it's opened in the bed mode, it may tip. Convert back to sofa mode before sitting on edge.
EDIT: Not selling mine unfortunately, just suggesting something that may fit your budget.