After considering my options, I decided that the best thing to do would be try and get the replacement parts from eBay.

I placed the order and a few days later had my nice new hinges.

I was quick to install my new hinges, and thus quick to find my new problem!

The new hinges lined up great with the holes in the frame, but it turns out the hinge was a bit bigger than the old one. And thus the problem revealed itself. Now the center of the futon was higher than the crossbars on the sides of the frame.

TODO Insert picture

I tried it out for a night and found that I really was rolling off the edges of the futon because of the slant.

Now a new problem to solve!