<p>Is it possible to set the title of a page when it's simply a loaded SWF?</p>

I would think you would be able to do it.  You would have to access the javascript DOM.
A couple links that may steer you down the correct path..
http://homepage.ntlworld.com/kayseycarvey/document2.html
http://www.permadi.com/tutorial/flashjscommand/