"The locally measured energy of any particle or photon changes (is "red-shifted" or blue-shifted) as it climbs out or falls into a static gravitational field."
The measurement part is correct but this is a consequence of the time dilation at the point where the observation is made and has nothing to do with 'photons' which, as we see from QED, are a phenomena associated with the interaction of EM energy only.
The other error in the paper is the assumption that a photon can be red-shifted. This is not so. The emission can be measured as red-shifted but this is consequence of time dilation (either at the emitter or detector) and has nothing to do with the EM wave or photon dynamics. In QED, if the amplitude of the wave changes between the emitter and absorber then the number of photons also changes (the number of photons is proportional to the square of the amplitude of the wave).
See the two papers I posted recently for further clarification of these points or the thread entitled 'On the Granularity of Photons' for an earlier draft of my position (a later and more accurate draft, No.5, will be available next week).
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