Using ASP.NET with AJAX and ARR Reverse Proxy

A few ASP.NET Web Forms applications, written a decade ago to much older standards (we brought them up from ASP.NET 1.1 to ASP.NET 4.0 only this past year), are being retrofit to get the real web server out of the DMZ and run as individual web sites on servers that are accessed only via an ARR reverse proxy. I would like to get them running with the minimum perturbation possible.
Things I can't control - the ARR itself - here's how it works:
What the user's browser requests: http://www.company.com/tools/locale/toolname/Main.aspx What the ARR reverse proxies to: http://toolname.company.com/locale/toolname/Main.aspx What the server code at the actual ...