Re-encode the video with SUPER, using these settings:
Note that the SUPER download page is hard to navigate and that SUPER installs some extra software if you don't pay attention to the questions during the install. Icky, but it does the job better than anything else I've found. (I also tried Handbrake and the software that came with the camera). Oh, here's instructions if you want know how to download SUPER.
The resulting file can be edited in VirtualDub.
I think (and hope) that there's a better way, but this one works.
Here's the video, incidentally:
The edit was just switching out the soundtrack.