We are also maintaining data in ESRI and moving it over to Intergraph CAD with I/Map Editor. I think there is a CAD version (9.3, maybe?) pre-requisite for the I/Map Editor toolbar, so we are waiting on our 911 center to get us a trial. My colleague was the one in the meeting, so I don't have all the details, but will try to keep you updated.
And, yes, working with Geomedia is very different than ESRI. We struggle most with labeling and extent because of the crazy process to create a new SVG symbol. However, I noticed that ArcGIS Pro seems to handle data connections like Geomedia does -- as in you have to connect to all your sources in each project.