What if you let the barrel dry out until gaps started to form. Then, you grind down the rivets and losen the bands a few at a time. Then drive some self tapping screws into each stave where the band sits on it and as you move on to each stave you close the gaps and drive another screw into each stave. In the end, you close up all the gaps and the self tapping screws will hold the straps and staves as well as the whole barrel together. Lots of work, but sounds like it would work in theory anyway.
Did I make any sense?:-D
I have now officially abandoned this project. I'm getting me some liquid smoke and George Foreman grill...