Clamps. By gods, they were the best investment that I've made so far. I am utterly besides myself in smugness for having bought those clamps.
I got the side bars put together easily enough, and then I put in the bottom brace easily enough. What I was left with was one shelf and two pegged-in back bars. If you follow what I said, what that means is that I have the bottom brace holding the whole thing together, which is phenomenally insecure and an invitation to failure. In order to work, I had to get those other braces in and secure, and I don't mean glue. You see, bamboo hates glue. I've had enough bad experiences with bamboo to know that I needed a mechanical solution.
My solution turned out to be a wide flat-headed screw-bolt. It's threading perfectly matched the pre-existing peg holes in the existing slats. All I needed to do was to extend the existing peg holes to accomodate the screw. Essentially, I used the existing holes as a drill guide. I then drilled a bigger hole through the side, so that the screw would not work on it. From there, it was just a matter of tightening.
The second bar had no drill holes, so to do that one, I had to start with the side piece and extend the peg hole through to the other side. I could then use that hole as a guide to drilling a hole into the slat. As I had to hold the slat while doing this, one side turned out perfect while the other was about 1/16th an inch off. All in all, unreasonablly good for all my limitations.
The result? Sturdy.
Next I need to do shelves, but that's just a matter of cutting down some boards. As long as I don't lose a finger, I should be good.