Ironically, much of Jung's criticism of Joyce would not have been applicable to Tolkien. As I said in my review of Jung's article on Ulysses:

It is evident that he does not see Joyce as an innovator because he finds him mired in a Medieval Catholic Irish world. His studied attempts at distancing himself from this background are like, in Jung’s words, the aristocratic Bolshevik who revels in not shaving. Silly and symbolic gestures are taken to remove the author from his background, but it only reinforces that he is still a slave to a particular mindset.

On a psychological level, the novel itself is also flawed. Although Jung believes that there is an attempt to associate with a dream world, he finds Joyce’s novel far too sober and everyday to effectively tap into the dream-consciousness of the reader. Likewise, although he sees clear association of the major characters to archetypes with which a reader can identify, the nature of the association is too shallow to have any real resonance.

Tolkien is certainly distanced enough from the background of his story, and his novel is likely effective at tapping into the "dream-consciousness" of the reader. You and Larry may disagree, but I feel that Tolkien's symbolism, while not subtle, is also rich enough and deep enough that Jung would have approved.