OK - I have a fix, but it's a little more complicated. I got an email request on this subject last night, so this will hopefully serve more than one purpose.
I use Flash quite a bit in skinning, and besides that I happen to LIKE Flash. I recently looked into the Microsoft eolas crap that changed the way inline objects are displayed in IE and found several fixes, most of which require injecting the Flash into a DIV using Javascript. I settled on the fix I found at Kirupa.com and it works well for me and my esteemed clients.
I used this method this evening to display a Flash file through the Text/HTML module then checked it in FireFox, and the SolPart menu is indeed displayed on top of the Flash - just as you want. It involves uploading a javascript file to the server, so unless you use FTP you'll need to add .js to the 'allowed filetypes' list.
First, go to http://www.kirupa.com/developer/flash8/flash_fix.htm and download the flashobject.js javascript file. Send this to your server. The code that the Kirupa page generates may need to be changed just a bit. My sample Flash file is named intro.swf and is 155px x 150px. My working code to enter into the Text/HTML module is:
<script type="text/javascript" src="flashobject.js"></script>
<div id="flashcontent" style="width: 155px; height: 150px"></div>
<script type="text/javascript"> var fo = new FlashObject("intro.swf", "animationName", "155", "150", "8", "#FFFFFF");
fo.addParam("allowScriptAccess", "sameDomain");
fo.addParam("quality", "high");
fo.addParam("scale", "noscale");
fo.addParam("loop", "false");
fo.addParam("WMode", "transparent");
fo.addParam("BGColor", "#FFFFFF");
fo.write("flashcontent");
</script>
The "8" in this code designates the Flash Player version required by the movie.
Hope this helps,