Yes, I meant to say "Team Foundation Server."
I was able to resolve this issue by applying "LocalHost" in place of the server name. Since the only thing that will differ between one server and the next is the server name (basic configurations and database name will remain constant), "LocalHost" works great and I'm able to avoid the headache of modifying the database connection manager's connection string in an expression by replacing the server name with the MachineName system variable.
Thanks.