Implimenting Facebook like in AS3 project

We are creating a pure AS3 project, and would like to implement connectivity to facebook, i.e. the using facebook's "like" functionality, and possibly more later on.  We have run into some problems, however.  Our swf is loaded onto the web page using SWFObject 2.2, embedded dynamically.  We can have the like button appear, and it works, but we can't have both on screen at any time: if the swf is loaded, the like button is not, and vice-versa.

We have tried setting the wmode of the swfObject to both opaque and transparent, with no joy.  As I understand it, we need to give the like button a greater z-index than the SWFObject, but by default they ignore z-indices.  It also doesn't seem possible to dynamically embed the swf within a <div>, as that requires javascript, which won't run in the div.  Static embedding of the swf isn't a feasible option, as we require access to javascript from our swf.

Is there a way for us to have our swf dynamically embedded, and have the 'like' button placed on top, that allows us full functionality of our javascript code?