At the agency I worked for in the federal government, we had a "dedicated" system too that had its own T1 lines run to the various field/Regional offices and HQ (usually installed in some conference room). But because there were so many teleconferences needed and going on between these various agency offices around the country, there were a number of contracts obtained over the years with various vendors like Cisco (WebEx) and others to allow for all types of audio & video teleconferencing to include outside entities. Even Windoze has its own internal Outlook conference call function.
And with respect to this court "moving ahead quickly" - well with Leon having a timeline where things aren't really getting started until December means he isn't exactly operating "quickly"... particularly given the nature of this particular issue. 
There's no "mucking" necessary with these telecon systems. Schedule the thing, give attendees the number to be called and the conference ID, and they can get connected - even if just audio-only.
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