Dan, i am not so familiar with TGM so i may be commenting out of turn here, but:
The main difference with stack n tilt i believe (sure i will be corrected) is the large focus on setting ones weight forward at address, thus preventing unnecessary lateral movement, thus making the golf swing more simple for average joes and the new people to the game. If this makes them play better and enjoy the game then thats what we want.
I guess the other philosiphies you speak of are traditional methods that have been used for generations.
For what its worth, i believe in trying things once and if it doesnt work then fine, ive lost nothing and had a go. Most people i assume would take parts of different swings to create their own swing.
Not sure if this is what your after but thought id add to the discussion.
Peace