I did find a better team within Amazon. I had an offer from one of the groups in AWS to do something right up my alley. It was basically a dream job. My manager blocked it. I appealed to HR and they simply ignored the "rules" (as they are in the handbook) and wouldn't let me leave.
So, one of the things-- the claim that you can go to another team if your manager doesn't perform-- turned out not to be true.
Rather than stay with a company that wasn't keeping its promises, I left. So, I can't speak to other teams. [2]
[1] Though 3 of the sibling teams at the same level, who reported to my bosses boss, were also run by bad guys, which cut off most of the obvious lateral transfers.
[2] It is possible things have improved, as it has been more than 3 years.