I just literally spent the better part of all day ripping apart HTML and CSS and seeing why one flash element is under a drop down menu and another flash element hides the menu despite the CSS being the same. And why one flash element simply disappears with wmode=transparent in IE but stays in FF. And why one flash element simply would not work with AC_FL_RunContent while another flash element runs just fine. Tore it apart, put it back together, stripped out the necessary pieces, ran side by side comparisons...
Turns out, my original hypothesis which the designers said COULD NOT POSSIBLY BE THE CASE was true all along. The problem was in the flash file. Got a designer to recreate it from scratch and, what do you know, dropped it into the unchanged copy of the page and it works! My entire day tearing things apart and putting them back together... digging a hole, filling it right back in.
Kill me now.