I've tried everything I can think of and google. Example here:
http://getc.thefstopdesign.com/the-horses/lzp-linnzel/
There are two copies of the video, one with ?wmode=transparent in the url (top) and the other with ?wmode=opaque and niether works. If you click on the image above them, the full size image (shadowbox) drops behind them both.
If they were closer to the top of the page, the dropdown menu items would go behind as well.
Having to add the transparent or opaque code to the url is already a problem because this is going to be a client managed site. It's hard for me to understand why, after all these years, we can't just embed a video in a way that just behaves properly by default.