Hello, I also had problems with the switch between Am and E and I did the same as you : I watched Lisa's thumb position and copied it, and it worked. I don't mute the low E string tough, I just anchor my thumb firmly on top of the neck between 2nd and 3rd fret. I think it is this firm anchor that helps, and now I make sure not to move my thumb when switching chords.
The only real failure is the failure to try.