There's no realistic way to get around this - it's not a limitation in the specs or anything like that, but in IE itself and presumably how the URL is allocated (I believe the limit is actually 2083 characters by the way, for some reason).
Since IE needs the URL all in one go to send to the server, I can't think of any clever tricks that would enable you to work around it. Some options I considered were to send the query parameters via POST instead of GET (but this is often not interchangeable on the server side, and the clients will treat this differently in that the URL can't then appear in a hyperlink or be bookmarked or entered manually, and if the user wants to refresh they'll get the "send information again" warning, which makes sense since POST is meant to update information on the remote server, and it'll only work if it's the query string pushing it beyond the limit rather than some ungodly URL). Alternatively you could perhaps chunk up the URL, setting the overflow part in a cookie and then making the request to the stub of the URL, which is intelligent enough to pull the context out of the cookie and append it to the URL actually received. However this again complicates processing on the server, probably far too much to be used beyond a trivial application, and also still means you can't put that URL in hyperlinks or bookmarks or whatever, since an important part of it is client state.
Basically, everything else would involve rewriting the server to somehow piece together the extra information, and if you're able to do this then you should be able to simply change the URL scheme so that everything's below 2000 characters. So no - no real way around it.
(Though if you could use something like tinyurl to act as a proxy rather than issuing a browser redirect to the URL, that could work).