Comment by JumpCrisscross

> shouldn’t it blueshift on the way in, gain some preposterous amount of energy — enough that it can escape

You're devilishly close to the Penrose process by which "energy can be extracted from a rotating black hole" [1]. (You can also make them explode [2].)

[1] https://en.wikipedia.org/wiki/Penrose_process

[2] https://en.wikipedia.org/wiki/Black_hole_bomb