Holy shit.
Okay, so: the one problem with my futon is that, because I took one with a wire mesh rather than bars, it was more prone to breaking. And break it did. It couldn't quite hold my weight if it was concentrated in one spot, so eventually the wires started breaking one by one, forming a couple of deep craters on the seat of the couch. I've been thinking about how to fix it for a while now.
JUST NOW I decided to visit work for no real reason and discovered some futon parts next to a dumpster. Seriously. Not even the whole thing. Just the frame and the arms of an obviously-used futon.
I brought them home and assembled my Frankencouch. Now I have the design that I like (the arms from my original) mixed with the frame that I need (the bar-frame from the parts I found). It doesn't transform quite as well, and it's not quite as comfortable, but it works!
Talk about lucky!
Now what should I do with the leftover bits? I'm thinking about hanging onto them, but I'm running low on space.