It's already a kind of well known concept in SciFi to bounce the photon back and forth a lot, getting a little hit of momentum each time (and draining its energ

It's already a kind of well known concept in SciFi to bounce the photon back and forth a lot, getting a little hit of momentum each time (and draining its energy, thus changing its wavelength). Keeping the reflecting pair on the rocket and trying to use asymmetry to pull more off on one side than the other seems a pretty straightforward thing to try.