So I know there have been a number of similar posts, but I think this is enough of a variation to warrant its own question:
I am building an XLS exporter in PHP and
It is possible to POST to a hidden iframe. Therefore, you don't need to worry about the length of the query string; you will post the key/value pairs which will generate your XLS file and subsequently force the file download to the browser.
UPDATE A quick Google search turned up this article: http://particletree.com/notebook/ajax-file-download-or-not/
Basically, the suggestion is to POST your form to the current page and respond with a file download. This alternative might be good enough for you.