According to our IT people, a middle-of-the-road server w/ a 3 years service agreement costs about 5 grand. (or 5000/36 moths = 139/month). The server would be available outside the company, but would be located in a network DMZ. We can have sudo, but can't mount any network filesystems. Giving outsiders privileged access to the server is apparently possible through some complicated process.
Apparently binding a DNS entry for a subdomain to an external server is quick and easy. So, why not get a virtual private server somewhere and avoid jumping through management hoops?
Here are a few providers I'm considering: