I had a couple of concerns: first, if you send source code/data/etc between your home and work PCs via this mechanism, it could be logged by or browsed at the mediation server over which you have no control.
Second, this system is subverting the intended function of the facility's firewall lockdown which I assume is done to preserve patient data confidentiality?
You're probably better off establishing an ipsec or other VPN connection under the sysop's aegis so he/she can document and oversee your access.
"... They ne'er cared for us
yet: suffer us to famish, and their store-houses
crammed with grain; make edicts for usury, to
support usurers; repeal daily any wholesome act
established against the rich, and provide more
piercing statutes daily, to chain up and restrain
the poor. If the wars eat us not up, they will; and
there's all the love they bear us."
-- Shakespeare: Coriolanus, Act 1, scene 1