Thanks for the ideas, Eric. I researched this issue quite a bit on the web and never found a solution. I messed with div index numbers and it didn't help. As near as I can determine, the QuickTime player simply insists on being on top (another web poster I found said this too) regardless of what you try to do. The best solution for me was to convert my videos from mp4 to flv (Flash). Then use the "wmode" parameter set to "opaque". There is a lot of info about this on the web. From what I read, "opaque" is the correct setting, not "transparent". Anyway, it works. Here's an example. outreach.php.
This said, if anyone has an example where they had success getting CSS drop-down menus to display on top of (not behind) a QuickTime video, I'd love to see it.