"The author charitably attributes the inability for such a system to be energy neutral to "engineering problems," but I think it's pretty clear that there are also physical laws that make this impossible."
Why not just use a electromagnetic system? Electons with mass down, and em-waves without mass up? Then it's not impossible, just very small forces and superconductors.
Failing that why not use quantum teleportation?
There are several ways to move a subatomic particle in a massless way, and then return it to having mass at a distance.
EDIT My point is to say that the specifics of the enginerring aren't the real question. The real question is "Why doesn't the essential CONCEPT work"?
Thanks to mass-energy equivalence, your choices for visualizing this are many. Perhaps the two easiest are: Physically lifting the 1kg matter+antimatter to elevation h, which is equivalent to Gravitational redshifting of the 1kg-worth (converted to energy) of photons between ground level and elevation h
As an aside, if momentum is conserved, shouldn't each photon be paired and emitted in opposite directions? The author charitably attributes the inability for such a system to be energy neutral to "engineering problems," but I think it's pretty clear that there are also physical laws that make this impossible.