However, if I click on the other screen, it freaks out and minimizes. If, however, I set it to OpenGL (and thereby have more aliasing... sigh) alt-tabbing works great.
If you tab out of a DirectX fullscreen application, Windows will automatically revert the resolution. In OpenGL, you have to do your own resolution management for which people usually don't build that functionality.
But the best part about HoN is that my left monitor is 2560x1080, and the game is rendered no wider than 16:9!
That's probably a balance issue. Players with wide monitors should not get an advantage by seeing more of the game action than others.