Go back to the 1931 cartoon "Bimbo's Initiation" by Fleischer Studios, which allegorically but also blatantly exposes the dark secret societies built around homosexual magick, illusion, coercion, mental shattering and rebuilding etc.
The cartoon proper has Bimbo walking along, falling into a manhole (underground initiation), then oddly being locked in there by Mickey Mouse (Hint hint).
But prior to that, the cartoon opens with an old timey college-style chant.
"WE ARE THE MEMBERS OF DO-IT-OR-DIE, D-I-D-I-D-I (or The Eye, The Eye, The Eye), WATCH US MAKE "BIMBO" AS EASY AS PIE, D-I-D-I-D-I"
It's worth watching the cartoon, keeping Alice/Wonderland/MKUltra/Monarch in mind.
However, having just rewatched the Ghost in the Machine Psywar video, I found it interesting that they specifically used the phrasing of "Do or die" in reference to being surrounded by people who say such a thing.
This is an avenue nobody has brought up.
It may be worth researching any historical usage of "Do or Die" or "Do it or die" in reference to societies, politicians, actors, etc.
Except that they clearly start with the D sound, not the I/Hi.
It's also done as a collegiate chant, referencing the recruitment process being directly tied to places like Yale, etc.
It's not done in any way that resembles the usual Calloway style scat of the era.
However, good connections on the rest, fren!