On the basis of that, I'm seeing Gary's 'White Rabbit', not as a nod or a wave to esoteric knowledge, which he was very probably aware of, but rather a nod to a modern 'initiation' and 'knowledge/ or deeper understanding', involving a structuralist and later, a structuralist and post-structuralist coalescence, which helps players to describe and structure fantasy worlds/ societies, which are then 'brought to life' by applying personal agency to the structure.
As no one will have read this far, I'm probably not going to have to defend that (and I decline to be sucked into Forge-land literary theory rather than scientific theory) but, to me, it adds up to a clearer understanding of what fed into D&D, while getting rid of any notion of Gary as a 'bumbling hippie who did good but tailed-off'. Instead, something of an expert in comparative mythology, a social scientist with an understanding of structure and modelling techniques, and an awareness of the tension between structure and personal agency.
I got to the end by skipping over some of the Golden Bough excerpts!
It's an interesting hypothesis you're putting forward, but I must confess that I personally don't feel the force of it.
First, the discussion of social formations in the DMG and UA (and the change-of-mind as to whether it is good or bad for the game to include a social-status system) doesn't seem to me to speak to a particularly sophisticated sociology. It's fairly generic, and pales in comparison to (for example) the discussion of social forms in Rolemaster Companion VI, which is clearly written by someone with a good undergraduate (or higher) training in sociology and world history.
Second, but related, the AD&D rules don't really involve players "describing and structuring" fantasy worlds and societies. An OD&D-style megadungeon is not a society, and is barely a world, and in any event doesn't evince a very rich structure in the sociological sense. And AD&D, in which the megadungeon looms less large, doesn't say much about structures at all.
Third, the alignment system does not demonstrate any particular familiarity with either moral philosophy or the sociology of morals. Law vs Chaos seems to be derived from Moorcock and others, who in turn draw upon various mythological traditions. The addition of Good and Evil I don't know the historical explanation for (ie who, if anyonem, influenced Gygax in that respect), but the resulting structure is not one which I've ever seen "brought to life" in any interesting way via player agency. The history of the game tends to suggest that it's a serious impediment to player agency, and indeed that seems to have been one of the main motivations for it - in the absence of a socially rich gameworld in which the PCs are embedded and the players emotionally invested, alignment establishes a game-mechanical pressure against players acting out anti-social fantasies.
Fourth, I think the classes and races - with their origins in Chainmail - reflect conventions of wargaming, with units of different types or classes, rather than an attempt to establish a structural framework which player agency brings to life. It's often asserted that "classes are archetypes", but I don't accept this. If classses really were archetypes, than Druids and Magic-Users would be the same class (Merlin, Taoist mystics, stereotypical witch-doctors, etc), as would Clerics and Paladins - and that's leaving to one side the highly questionable notion that "medieaval Christian warrior" is some sort of archetype at all, as opposed to a rather parochial phenomenon of the European Middle Ages.
Undoubtedly Gygax was familiar with a wide range of myths, legends and history. So was REH. But to in my opinion there is little of sociological (as opposed to aesthetic) merit in REH's work, and I find the same to be true of D&D.