Etymology of 'Pizzazz'

OED has

Frequently attributed to D. Vreeland (1906–89), who became fashion editor of Harper's Bazaar in 1937, but compare [an NY Times quotation] (26 February), which cites the March issue of Harper's Bazaar (see below). The term is not found in issues of the Lampoon of that date.

1937 Harper's Bazaar Mar. 116 (heading) Pizazz, to quote the editor of the Harvard Lampoon, is an indefinable dynamic quality, the je ne sais quoi of function; as, for instance, adding Scotch puts the pizazz into a drink. Certain clothes have it, too...There's pizazz in this rust evening coat, swinging wide in back, jutting crazily over the shoulders.

... which does correspond to two of the sources you researched.

It's not unknown for OED to be trumped in its earliest citations, but it does appear to have been coined by Diana Vreeland.

Some slightly different meanings of pizzazz have been found earlier than 1937.

The Grammarphobia Blog says:

The noun “pizzazz” (also spelled “pizazz” and “pazazz”) originated in the 1910s and originally meant an expert or an exemplar, according to Cassell’s Dictionary of Slang. (This was news to me too!)

In the 1920s, the meaning evolved into style, glamour, or ostentation. By the 1930s, it was being used to mean energy or zest. I’d guess this is the meaning in the expression “full of pizzazz.”

The word’s etymology is unknown, though the Oxford English Dictionary says it’s frequently attributed to Diana Vreeland, the late fashion maven. (Cassell’s Dictionary of Word and Phrase Origins is dubious about the Vreeland attribution.) ...

Although its origin is unknown, “pizzazz” has echoes in “razzle” (a spree or a good time) and “razzmatazz” (showy, high-class, or an exclamation of pleasure). I think people back then had a lot more energy than we do today.

And via the American Dialect Society Email Discussion List, Wordorigins.org has:

There is an earlier use of pizzazz, in a different sense. From the 7 December 1913 Mansfield [Ohio] News:

Brother Russell declared, bo, that his crowd had already framed it up with some of the big guys in the music world to put the kibosh on this line of junk, and that it was only a question of time before they would have such pieces as “When I Get You Alone Tonight” completely on the pizzazz.

What relation this musical slang usage has with the more modern one is uncertain.