Jim:

Just a few "corrections", mostly for the sake of other readers (if there are any, by now).

There is no "basic premise of GR" stating "that geodesic motion is uniform motion." It is correct to say that geodesic motion ("free fall") is the closest thing to "uniform motion" one may find within General Relativity. But that's not the same as saying they are the same thing.

Also, within GR one really cannot talk about "kinetic energy" as if it was isolable. In fact, even the Special Relativistic concept of mass-energy has trouble being isolated. It's really all a part of the mass-energy-momentum-stress tensor (though one can look at various components in appropriately chosen coordinate systems, or by way of various assumed forms of matter and/or energy, to see that such contains all that has previously been designated via various separate treatments).

David

P.S. I haven't bothered to read the reference you link to, since it is not relevant to your "two-choice dilemma". However, it is quite possible (though I cannot be certain without reading it) that the "positive pressure" and "flow of energy" you deride actually pertains to the mass-energy-momentum-stress tensor, that is the source term in Einstein's field equation(s), rather than some supposed aspects of gravity itself. But as I say, that's not relevant to the core discussion.