Somehow the Klymit hadn't come up in my searches before. $133 is dirt-cheap, and for that price it isn't worth making my own. The Klymit won't handle anything technical, but I'm only interested in flatwater anyway. Add a cheap paddle and a MTI Journey and the entire setup is 5 pounds and $200, not bad at all. Lighter than a portable suspension bridge.
Also, upon further reflection, the geometry of mapping flat fabric into curving tubes is pretty complicated - the actual construction of the raft shape is more than I feel like dealing with. I'll leave it to the pros. I still kind of want to try the idea, a little, if only because I like the idea of all that redundancy. And because it would be kind of hilarious blowing up 50 balloons and stuffing them inside it. Maybe I'll make one out of my cheap cordura for canyoneering (as in, for actually using inside of the canyons, to avoid swims).
For future reference, if anyone finds this thread and decides to go with this crazy idea, I also considered bicycle tubes. It's another option, but probably too heavy for the amount of air compared with balloons, and difficult to find one that would go all the way around the raft (you might need a 36" unicycle tube or something).