If you cannot track the adwords campaigns before they are redirected to remove the tracking query strings, then you'll have to get rid of the "remove query strings" function here. As a result, you will risk having duplicate content in those search engines which do not recognize these query strings for what they are.
A better approach for the long term might be to move your tracking function into a script, and then add code to call that script before redirecting to remove the query string. The script itself could do the redirects, or you could call the script from .htaccess if you have server configuration access and can use RewriteMaps.
With the current set-up, there is really no good way to resolve the duplicate content problem and preserve tracking strings at the same time.