I'm not sure I understand. You seem to be suggesting:
"No union victory is bigger than the first win in the United States at Amazon, which Amazon many union leaders regard as an existential threat to labor standards across the economy because it touches so many industries and frequently dominates them."
But that's absolutely terrible, so you must be suggesting something else.
> "[...] which company many union leaders regard [...]"
Ergo:
No union victory is bigger than the first win in the United States at Amazon, which company many union leaders regard as an existential threat to labor standards across the economy because it touches so many industries and frequently dominates them
[EDIT] I also intentionally used the construction in my original post: "[...] which technique is usually overkill [...]". The usage there, unlike in the Times sentence, was actually necessary since the antecedent was too far removed. The original Times sentence was correct, but splitting it up or specifying the antecedent would remove the possibility of a reader being confused by thinking the Times writer wasn't, correctly, using "which" to refer to the closest antecedent ("Amazon") but instead to something earlier in the first clause ("first win").
On looking closer, I think it's the construction of that first clause that makes the "which" read like it might have been employed incorrectly, when it was (technically, kind of) not. "first win in the United States at Amazon". The "at" makes "Amazon" seem heavily dependent on "first win in the United States", so it still looks like "which" might point at "first win", not "Amazon".
That's obviously what you wrote, so I don't know why I replaced "company" with "Amazon" in my head. That's definitely better. Sorry for the confusion and thanks for not biting my head off where I deserved it.
"No union victory is bigger than the first win in the United States at Amazon, which Amazon many union leaders regard as an existential threat to labor standards across the economy because it touches so many industries and frequently dominates them."
But that's absolutely terrible, so you must be suggesting something else.