I keep going into the options to make the camera "Character Mode", but it immediately reverts to "Strategy Mode". There's no save button, so I can see why it isn't taking effect, but even going back to the main menu and changing it from there (it seems to save that preference) doesn't change it in-game. Any ideas?

I've had this too. I wonder if it's related to the fact that going into the menu resets the UI?

You can test this yourself by changing the positions of the onscreen toolbars then going into options. Which wouldn't be such a problem but the default layout has toolbars fighting for space.