Adventures in CSS: Success with New Design
After trying to get my layout to work one way without success, I've changed my layout.
The problem was that, in smaller browser windows, the flash movie would crowd out the side bar in unpleasant ways. I tried using percentage for the dimensions of the movie, but that behaved differently in every browser I tested it in...not a good sign for the browsers I hadn't tested in.

So, in all pages with flash movies as the content, I've modified the side bar. Some of the information in the side bar is now in a "top bar", some is in the "what's going on here" section, and part is still in the side bar which is now below the movie.

I'm implementing it now :-)