On the eHealth Forum, we’ve just started to experiment a bit with Zui.nz. This is an NZ based video calling / conferencing service based on the open source jistsi.org platform. We are in the early days of this at the moment.
Yes it does have recording capability. I think it can do this a number of ways, including locally (which is probably what we need). It even has the potential to livestream to YouTube.com, and use that for sharing if need be. But it would need some setup to achieve that.
It is the brainchild of the awesome @Ben_Gray and several of his techie mates, and I understand that in addition to the free zui.nz service, it can be rebadged and supported by them commercially.