iFinity

That's not exactly how it all works.

THe Url Rewriting means that you can have a page called 'burgerking' : but this will resolve only to a particular DNN page - it won't rewrite the restid/ source/ etc parts to the url.

If you replace the Url value in the page settings, this doesn't actually replace the url.  All this function does in DNN is submit that url when you click on the 'burger king' page in the DNN menu.  If you request 'burgerking' directly, it doesn't show the url you inserted, it will just resolve to a (probably) empty page.

The Url Master module has an option to change this default DNN behaviour by doing a 301 or 302 redirect to the inserted url when you request the 'burgerking' url, but this is not the same thing as rewriting the page as I think you want to do.

Well, that links resolves, but only through a redirect.  A redirect from a short url to a long one has little SEO benefit (if any).  You can configure the Url Master module to do the same things as DNN is doing (redirect from the url to the page) but you're not going to be able to setup the url to work the way you expect.  The problem you have is that you need to rewrite extra information into the url, and there's no construct to do that.