I was not able to get the movie to load but I was able to see the menus not going over the top of this area. Like you mentioned the wmode parameter should only apply to Flash, and it would need to be set to transparent.
The other thing I would try is to make a new div to put the movie in. For the style that is applied to this div you should try adjusting the positioning and the z-index. It is likely a combination of these settings that are causing the menus to go behind it. You will need to ensure that the positioning is the same as your menu and that the z-index is lower that that level of the menu. The higher z-index will appear on top.