Aero is disabled on my PC (I use Classic Windows theme), so I didn't try playing with that.
Game Capture does what I want - minus the mouse cursor problem.
Software Capture shows people when I alt+tab and that's bad. If I specify Software Capture to use Window Capture with the game's .exe, it doesn't change anything and behaves the same as with Monitor Capture.
I just tried enabling the new standard Windows 7 theme with Aero and play around with the settings and it still shows all other windows that are on top of the game.