It's not a problem, I quite enjoyed the challenge but it is a lot harder than I'd initially anticipated.
Assuming your LMS and Adapt content are being served from the same domain, the extension will inject javascript and styling into the iframe parent window and put some javascript and styling fixes into Adapt in the iframe content. So, yes it can be treated as a normal extension for installation and should 'just work' i.e. it'll make the parent iframe responsive. (I'm pretty sure it'll break the Authoring Tool though, as there is no schema - yet).
The extension is built in two stages. There are a series of styling and javascript fixes, these will have an effect on all containing iframes, in all browsers and will make the containing iframe responsive (on the assumption that the iframe should fill the window, i.e. that it is a full height + width iframe). The second stage is a preliminary attempt to overcome the iOS Safari problems, and that is the bit which isn't yet finished.
The last real iOS hitch is implementing my fake scrolling idea across all elements which require scrolling in Adapt. I'll have to build a little library to do this, but it is possible (in theory) to reimplement scrolling inside iframes using css 3d translation effects and a couple of touchstart/touchmove event handlers to capture the movement.
Testing, help and advice are always appreciated :D thanks for the friendly nudges!
Oh, the index.html file in the extension is really simple iframe for testing the fixes. Just build adapt and run it through that file or your own iframe file.