What do people recommend doing in this situation? Walk away? Reschedule? Insist on explanation? Or is it feasible they would make a decision without the manager interview.
Should you ever have a truly terrible experience in interview, first tell them that you are going to have to call a halt so as to not waste any more time.
Then inform them that you are very sorry, but unfortunately they have managed to fail the interview process and should the chance to employ you come around again, could they please not reapply.
Then walk away.
I have only done this once, while being told about the extra unpaid hours I would have to put in because of 'culture'.
It was more than worth it though, as I got to see a shade of maroon that I was previously unaware was even within the gamut of normal human skin tones.
But if the company has no second thought about wasting time of candidates then I would stop asking myself how to "get in" and instead ask myself if they really need me.
Call me spoiled, but I'm not going to jump through hoops (like more than three interviews) and accept abuse just for the honour to serve. I am not a slave, and if my skills have some value then I will eventually find a company that actually needs them.
In a company the size of Amazon, there is always someone else who can step in. If not, it has serious management issues.