You gain even more momentum from reflecting the light back into the black hole! When you absorb a photon, you gain its momentum. However, when you reflect a photon, you gain twice its momentum to account for the momentum possessed by the photon now flying away from you.

Isn't that a three-fer?

You first emit the photon towards the black hole, momentum gain. Absorbing the photon on the return would be a two-fer, and reflecting a three-fer.

Absorbing the photon would be a two-fer. Reflecting it is just starting the next two-fer. It's two-fers all the way down.

Ooh. Even better, it's like compound interest.

You emit photon 1. It has momentum m. It comes back blueshifted, so you get momentum km, with k > 1. You reflect that back, and you get momentum k^2m...

It's not that simple, because as you start to move away, you redshift the photons you reflect. And the alignment issues are going to be pretty severe. And if you get too much compound interest, the photons may be blue-shifted enough to kill you or damage your ship. Still, the idea is pretty slick.

Also in all slingshot maneuvers you get more the closer you are, so you wanna pour in the most energy the closest you can get.