As an aside, and strictly as an opinion, I think your firewall adminstrator isn't understanding what is being asked.
In an internal LAN, it is rather extreme to lock a firewall down such that it wants one port in and one port out. One port in might make sense if for nothing else than tracking the inbound, but once you've accepted the requests from that port, it really shouldn't matter what the destination port is (stateful firewall). You prioritize getting the information to the destination and want to make sure it always gets there no matter what, once you've designated it as allowed via the inbound port. If you ever go to Unity or Web client you're likely to run into the same issue, as Hyland is pushing toward the application server methodology rather than local ODBC. (Speaking of, do you use either client today and do they work ok?)
If they are convinced stateful firewall is enabled then there the issue resides with the trust between the two firewalls. The second firewall is not properly funneling the data through. It would probably work if your first firewall had inbound port isolated with stateful enabled, and the second firewall open but configured to receive traffic only from the first firewall.
