Origin of "wannabe" and its precursors
Solution 1:
I'd presume that "wannabe" as an adjective comes from slurring the earlier phrase "want-to-be" into a single word. Thus, your 1936 reference. This is a common mechanism of linguistic evolution.
Turning the adjective form into a stand-alone noun form per the OED reference is then a different but even more common linguistic mechanism. You can see that in the initial citation, where "a Jimmy Cagney wannabe" is a rephrasing of "a wannabe Jimmy Cagney" with the adjective and noun swapped to form a different emphasis.
Thus, I believe you've traced it correctly; the noun is an outgrowth of the initial adjectival phrase, not a coincidental parallel evolution.
Solution 2:
Use of want-to-be/wanta-be/wannabe as a noun goes back very far indeed, chiefly in the form want-to-be['s]." It seems fair to say that the late 1970s/early 1980s popularization of the expression owes very little to any tradition of use of the term as a noun, but you could also make the case that want-to-be/wanta-be/wannabe as a noun has been with us for more than 150 years.
The earliest match for the noun form of the word that I found in a series of Elephind searches is from "Daring to Do," in the [Philadelphia, Pennsylvania] American Presbyterian (October 3, 1861), reprinted from Hall's Journal of Health, a New York City publication:
Small minds spend a good deal of time in deciding, as to a particular course of conduct; whether "they can afford to do it." "What will Mrs. Grundy say?" is a question of momentous interest. To do anything which Mrs. Upstart or the Smith's would consider "mean," is no more to be thought of, than committing a petty larceny, and being found out. It is known that any of the Want-to-be's would almost as lief be found coming out of a hen-roost at midnight, as to live in any street having "East" attached to it; while there are those who feel forty feet higher, by reason of their being able to say, "I live in Fifth Avenue:" and for such to be seen with a bundle or package in the hand on Broadway! they would fairly tremble in their shoes, lest they might be recognised by some one into whose "set" they were aiming to obtain an entrée.
From a headline in the Scranton [Pennsylvania] Tribune (March 2, 1898):
The Want-to-Be's Hold a Conference: Democratic Poor Directors-Elect Discuss Ways and Means: Want to Oust the Present Body: Four of the Aspiring Democrats Met Last Night--Quo Warranto Proceedings to Be Started Soon, but There Is a Hitch Over the Time and Method--Directors-Elect Will Soon Confer with Their Attorney, I. H. Burns
From "Valley League Diamond Series," in the [Phoenix] Arizona Republican (January 5, 1913):
The facility with which Luther McCarty fools a fan while in training seems to be equalled only by his ability to go home with the bacon after the bout. Six months ago, he was spoken of as a big dub, stuck on his own looks and not of sufficient class to get out of the Carl Morris division of wanta-be's. Yet in three weeks, he has humbled the two leading heavyweight pugilists of the country, one of whom has been a crusher of white hopes for years, and the other of whom was looked upon as the heavyweight velocipede to roll out the black business in pugilism.
From "Support the Soldier Candidates: Women of Queensland! Fight for Those Who Fought for You," in the [Brisbane, Queensland] National Leader (February 22, 1918):
It will be put up to you time after time that the soldier men's forte is fighting, and that a different class of brains is required for parliamentary work. That's the sort of guff and griffle the old has-beens, the ancient want-to-be's, and the slow-down Laborites are starring in the press and from the platform. Don't you listen to them. Think it out for yourselves.
From Annie Laurie, "Is She Not Party to This Murder?" in the Santa Cruz [California] Evening News (September 24, 1919):
And in the name of common sense, if we must hear of this woman, and women like her, let's not talk about the "lure of the vampire"—let's leave that to the writers of the lines in the movies.
Let's simply call them what they are—
They are not sirens—they are just "Want-to-be's," that's all.
From "[]Slovaks Break Record](https://news.hrvh.org/veridian/cgi-bin/senylrc?a=d&d=rocklandctytimes19340804.1.4&txq=%22want-to-be%22)," in the [Haverstraw, New York] Rockland County Times (August 4, 1934):
Besides the tug of war, in which Michael Hylas was anchor man for the married men and John Urban for the want-to-be, there was a horseshoe pitching contest, won by Frank Rose and John Rosinsky. Other features were sack races, three-legged races, baseball and numerous other events.
And from "A World of Illusion," in the Cessnock [New South Wales] Eagle and South Maitland Recorder (September 13, 1949):
It's a good story which probably has no moral. To read it, leads us into the land of "want-to-be" where there is no good, except in the escape from truth in[to] imagination. Imagine long enough and one begins to wait for to-morrow. Wait long enough and one companies with illusion.
As an adjective, "want-to-be" is even older. The earliest Elephind match for this form of the term is from "Protestant League in Boston!" in the [Cincinnati, Ohio] Catholic Telegraph (April 15, 1843):
It is not they thus behold their clergy there; they see them reft of all earthly ties and devoting their youth and age to the service of God: they meet them at the couch of sickness and the hearth of poverty, pouring out the consolations of hope and faith. They would justly look with horror upon the creed that would tolerate such luxurious sinfulness, as mark the lives of the gallant and lady-killing Kirk, and his thirty-seven married or want-to-be married associates.