We need to be able to run two versions of one ASP.net web application on the same intranet server and port number, but with one mapped to / and the other mapped to /experimental
Can you run one of the sites at a different subdomain, say test1.organization.com and beta1.organization.com? If so then you can set them both up as top-level websites in IIS and set the Host Name on each Site Binding so they can both run on the same IP address and port.