SRFax lists healthcare solutions on its site, and Faxage says "All of our fax service plans come with HIPAA compliance standard - No need for a 'special' plan or to pay extra for HIPAA related security features" and you can contact them for a BAA.
Other than that you can do things in-house with Hylafax and either hardware (e.g. Mainpine boards, expensive but they Just Work) or software solutions. My experience with software solutions (IAXModem with Hylafax and Asterisk) has been that speeds and reliability are sometimes poor, at least compared to good hardware solutions or physical fax machines supporting 33.6k.
HylaFAX Enterprise is a full SW solution, (roughly) HylaFAX plus the Dialogic SR140 which does both T.38 (new school fax) and G.711 (old school telephony fax). But generally it's 14.4k - believe it or not V.34 (33.6k) is still somewhat experimental over IP.
And 9600 is usually required to get faxes through to a lot of places, because everyone is trying to do fax over VoIP, and that is generally tough sledding, if it's possible at all.
Other than that you can do things in-house with Hylafax and either hardware (e.g. Mainpine boards, expensive but they Just Work) or software solutions. My experience with software solutions (IAXModem with Hylafax and Asterisk) has been that speeds and reliability are sometimes poor, at least compared to good hardware solutions or physical fax machines supporting 33.6k.