Sounds like we have similar problems, and solutions! We also looked at Prism, but decided that we would only push the web client. As I am responsible for the training, having one supported client is best!
The issue we face here is that our PCs are not locked down. Anyone can install and use any app. So, I can't ensure that everyone uses Firefox.
Further, we are strongly recommending training for a consistent message, but I'm not sure if we will end up with mandatory training...
Your C# app sounds wonderful. You have your authentication tied in to their desktop. We aren't there yet... Working on it!