I really disagree with your disposition that 3D Super Mario games are not real Super Mario games.
While 2D are simply more fun due to the platforming purity, 3D games have an amazing feeling about them. Mario, unlike untold number of other 2D greats, was capable of coming to 3D with thunderous applause. SM64 and the Galaxy twins are simply fantastic games that really defined their presentations and gameplay styles.
Sunshine was just a bad concept and more of a adventure that platforming game IMO. So maybe it can remain on the fake list.
However, the other three had the Super Mario essence and quality.