While I do not agree with your points, your argument is viable on all of the other accounts than the one about 237. Kubrick's films deserve critical study, make no mistake; but, Room 237 is far from legitimate scholarship. The "critics" they selected provided terrible evidence for fantastic claims.
The highlights:
-The Shining was Kubrick's confession to contributing to the faked moon landing.
-Stanley Kubrick added his face onto the clouds in the opening crawl.
-And the film was a dissection of the Holocaust (based on the presence of excessive luggage when the Torrances enter the hotel, and Kubrick's conflicting desire to make a film on said event.)
In short, the "scholarship" in the documentary is terrible; it gives close reading a terrible, terrible name. Truth be told, posters on this forum (such as CCOnn) provide better written, thought, and researched arguments than all of the contributors to the film combined.
Again, while the rest of your post is viable, I disagreed with the boosting of Room 237.