Tricky, since most of these apps which can run in IE6 but not IE7 do bad things in JavaScript too. That means you can't just fix CSS issues in a proxy, because even if you could document every IE6 bug and how to fix it for IE7, the page could still change after it is loaded in the browser.
Then you could upgrade $(Initech) to IE7/Firefox, and slap the proxy between the users and the legacy web apps, and everybody's happy. When the internal developers upgrade the legacy web app, they can either keep it on the un-IE6-proxy, or upgrade its output and lose the proxy. IE6 can go away, we can stop wasting time with IE6 compatibility, everybody's happy, world peace, the end.
Disclaimer: I don't understand the nature of IE6 bugs very well at all, and I don't know if this is turing-complete or AI-complete or what.