It would be nice to use only Alt+Tab (without pressing Enter) to change the focus.

The proposed method would change the focus when Alt is not longer pressed. Once the menu is displayed, Alt+Tab can be used to go to the item in the menu (observe that actually only Tab is pressed again since Alt is continuously pressed). And Alt+Shift+Tab for the previous item. In order to cancel, ESC can be used (while pressing Alt). This is the default behavior in kde, for example.

I believe it is faster and uses less hand movements.