For anyone else running into the same problem, I just copied my HipChat.app in /Applications, and ran the second hipchat next to the first hipchat (you can also change the second hipchat's icon for easy distinguishment). It's not perfect (upon logout/restart it still remembers the preferences for the other instance), but it solved 90% of my hassle.
This has been driving me crazy for months, I had one version of the old buggy Adobe Air app running and one of the new Native app. Somehow just creating a copy of the new native app just never occurred to me. You just made my day substantially better.
That's smart. But still, it's crazy that something like multiple organizations would require you to do this on your end. There are better options out there :)
