Yeah, I wonder if that's part of the confusion. "Signing Bonus" is a weird name for what amounts to a large salary boost for the first 2 years. I think a lot of people think of a signing bonus as a lump sum you get when you are hired.

First sign on was ~25% of my base salary, and ~15% for every subsequent year.

That does change the math if Amazon is giving $100k bonuses each year for the first two years.