"it needs to be reflected where Earth is going to be; a much harder problem"
The relative velocity of the ancient Earth, black hole, and present earth would also need to coincide in such a way that you'd get a continuous (or, less desirably, periodic) stream of photons making the complete round-trip. Such a coincidence seems pretty unlikely.
Actually it seems pretty inevitable. Light is sprayed across the black hole from Earth; some of it ends up in every possible trajectory; some ends up in the critical 'orbit window' to be reflected back to where earth is going to be.
The relative velocity of the ancient Earth, black hole, and present earth would also need to coincide in such a way that you'd get a continuous (or, less desirably, periodic) stream of photons making the complete round-trip. Such a coincidence seems pretty unlikely.
Its a nice idea though.