If I understand you correctly (yes, I did read the material at the links, too), the functionality already exists within the plugin to select a Theme based on the GET parameter, as you call it, which the plugin refers to as a Query.
The problem occurs when the visitor clicks on a link within the iframe'd WordPress "webpage". That GET parameter is not passed.
I did some testing and found out one useful fact: if you click a link within the iframe'ed page, the referring URL of the Frame retains the GET parameter.
The next step will be to see what I can "see" from within the plugin via PHP values.
It is late now and time to get some sleep, but as soon as I get some time tomorrow, I will explore the possibilities. Mainly in the direction of seeing if I can provide a way within the plugin settings to specify the ?theme=2012 in your original post: <iframe width=100% height=100% src="http://www.somesite.com/page?theme=2012"></iframe> and have the plugin "see" that ?theme=2012 as long as the visitor remains in the iframe.
Sorry that I didn't think of this earlier, but I've never previously explored what PHP lets you look at when you are inside an iframe.