As much as I hate to throw in the towel, I think I might just have to suck it up and buy another rack. I don't have the tools to fabricate a stronger mounting piece, and I wouldn't know where to start even if I did. Even if I could get the rack to work properly, it looks like I won't be able to fit fenders on under it with my 700x35c tires. The rack itself is so freaking skinny on top.
I think I might go with the Topeak Explorer Disc rack and use p-clamps. My wife has the non-disc version and the quality seems good. I think the fenders are going to be a pain to mount with that one, too. Argh...