Here's a daft idea - not even good enough to call "half-baked" in that I don't know if it will work or how exactly to implement it.
Those "Your download should begin shortly" pages - where the page is displayed and then the file starts downloading. I think it's something to do with a multiplart http request (a multipart MIME type, the download page in the first part, and the file in the second part).
Have a third part which is also HTML, which, when it's loaded, makes a request to a "confirmation" script, including an appropriate ID for identifying the file. All going well, that confirmation signal will only be sent if the user's client actually received the third part of the response (and, therefore, the entirety of the second).
I'm not making much sense, am I? I've gotta sleep....