"It follows that a photon would be at A and B at the same time, in its own F of R."

Yes, Bill, fascinating isn't it. Theory does appear to lead to that conclusion - that each photon (in its own frame of reference, as you say) must exist at every point in the universe; and one might say that they inhabit eternity. A discussion here that you might find interesting:

http://www.thenakedscientists.com/forum/index.php?topic=18981

"Time is what prevents everything from happening at once" - John Wheeler