Well, it seems possible, but I'm still trying to figure out the object hierarchy. I've never had to change anything with embeds. It seems that the <object> wrapper hides the embed tag inside it and you can't access it. The embed doesn't even show up in the document's hierarchy when I output it unless I remove the <object> tags.
I'm able to access the embed's properties when I remove the object stuff, but that'll make it incompatible with some browsers. Embeds also don't seem to refresh when their properties change; I'm sure there's a way to force them to, but without the object wrapper this route is probably bad.
Now that I've examined this a bit more, this looks like something that should be done with layers. Each time the use clicks on one of the radio buttons, just move the appropriate layer to the top. :/
EDIT: I'll ask some of my l33t cr3w about this.