If you still want to throw your life away on a meaningless endeavor do not bring me along with you. Talking to management can and will hurt people. Do not make decisions for others without their consent.
Anecdotally, I think I hear the "I will die on this hill" variant more than the converse.
This does not hold. The hills in question were numbered arbitrarily. They had no value. We threw away lives to capture them only to give them up immediately. It was a pointless exercise. The phrase references this pointlessness. Attempting to assign meaning to the hill betrays a complete misunderstanding of both the history and the lesson.
If it is a misunderstanding, that is. While all sources I've seen sdo agree the phrase is of military origin, the Ngram shows usage as early as 1908 [1], with usage between 1930 and 1955 in English fiction [2]. Maybe the origin of the phrase predates the pointless numbered hills of the Vietnam War, and perhaps those hills had value and were worth dying on.
Not that this is a hill I'm willing to die on, though. All I wanted to point out is that the opposite phrase is used often per past experience, and Google Trends [3]. I can't actually find any trend data for the "original," but it is used.
[1] https://books.google.com/ngrams/graph?content=hill+to+die+on...
[2] https://books.google.com/ngrams/graph?content=hill+to+die+on...
[3] https://trends.google.com/trends/explore?date=all&geo=US&q=w...
A quick Google search would reveal that "This is a hill I will die on" is in fact an extremely common saying.