I unfortunately cannot provide you with any resource. I do understand your dilemma, I work with the same sort of set up. I have to take ESRI data and bring it into a Geomedia map for dispatching services. I currently use a series of models that were built by someone in the position over 7 years ago.
Lucky for me they are still functioning. I have made some small tweaks to a couple of the models but so far have left them in tact.
I'm not sure what data you are having to bring into the Geomedia environment. There is next to no support from the Geomedia and no community support around.