Man that's a tricky one...
First blush: create a new div that is all white and covers the entire screen and is z-indexed at like 10000 to make sure it covers the entire screen (divA). Then create another div on top of that one (divB), then find the FORM node on the DOM and change it's parent to divB. This would do what you say ie., leave the entire page intact, but hidden behind your new stuff and the form drawn out in the "new front" of the page.
Never done anything like it, but there's not reason that I can see immediately that it couldn't be done.
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BTW - I can assist with the JS, but don't have time to just experiment with building that one for you mate

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