What would be recommended as an authentication solution for a Software-as-a-service product?

Specifically, my product would have clients that would typically have low information technology skills, potentially not even having an IT department within their organization. I would still like to have my application authenticate against their internal directory service (eDirectory, Active Directory, etc.). I don't want them, however, to have to open/forward ports (for instance, opening up port 636 so I can do LDAPS binds directly to their directory service).

One idea I had was to have an application installed on a server within their organization's network that would backconnect to my service. This would be a persistant socket. When I need to authenticate a user, I send the credentials via the socket (encrypted) - the application then performs a bind/whatever to authenticate against the directory service and replies with OK/FAIL.

What would you suggest? My goal here is to essentially have the client install an application within their network, with very little configuration or intervention.