Yeah, github enterprise definitely makes sense, and it is something that we will look into.
Chrome's notifications since v28 kinda suck. Browser notifications have always been difficult, and in fact our www.trou.pe native app was originally just a toolbar app to solve this problem.
...slightly offtopic, on the alerts: chrome's rich notifications pop under apple's desktop notifications, and neither let me capture the notification and have the system voice read it to me rather than flash up in a corner that I'm not looking at. But campfire's in-browser notifications are the worst of all, some random tab beeping when I have 100 open.