What events led to the nearly universal acceptance of the letter "z" as the denotation of redshift? What did the letter originally stand for?
It may be that someone will come along with a better answer, but the first example I can find for the use of "z" explicitly for redshift is is William de Sitter's 1934 paper.
I'm tempted to think this is one of the earliest uses if not the first use, certainly looking at de Sitter's 1933 book where he touches on this briefly, he does not use the letter "z". However he did use "z" in a 1930 paper to represent the ratio between the radius of the Universe and initial radius, which in this context is actually the same quantity as 1 + z and so why he would've used "z" in his 1934 paper.
If I had to hazard a guess, there is no particular reason for the choice of "z" for redshift, it was just a convenient letter to use for the variable.