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.
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.