Thanks to you all for your many good suggestions, but I thought I'd share how I actually got these nuts off today. First, more PB Blaster, and then while I was at the auto parts store getting parts for another project, I spotted these and decided to try them:
On the package they say "Reusable" but on the store's web site they say "Disposable" so my hopes weren't really high. However, I used it and it did the trick. Essentially, it's a 6-point adapter that fits into a 12-point box-end wrench 2mm larger than the target size. So for my 13mm bolt, I used a 15mm wrench. It's sufficiently low profile that it was able to fit where more conventional extractors probably wouldn't.
I tried the first one and was elated when it actually broke the nut free, so I tried it on the second one, where it promptly cracked into pieces. Still, it seemed to me to be worth the $10 that I paid for the set, so I went back to the store and bought another set. As you can see from the picture above, the second nut was also removed and was tightly lodged in the extractor. I was able to remove the nut eventually, but there is now a significant crack in the side of the extractor, which leads me to conclude that I haven't many uses left with this one.
So my conclusion is that these are better thought of as "disposable" than "reusable" although some reuse is probably possible. Copious amounts of penetrating oil and the German opera on the radio probably both helped, but the tool did what I needed and I consider the price worth the avoided headaches of alternative means.