Dear Steve,
In 1960, before you were born, I published my one and only Phys. Rev. paper, "Generalization of Quantum Mechanics." I guess I was a quantumologist then, without knowing it. But, needless to say, I failed to revolutionize quantumology.
I do not know about those other two dimensions expanding that you speak of. That's not standard 1905 SRT in any case. And about needing "to account for that change," I am also at sea. Account how? The moving clock has already been set in a certain way. Are we to reset it, or does it reset itself? In any case, we agree "that GPS clocks time more slowly according to their relative velocities" -- provided we are talking about proper time and uncompensated clocks. If the clocks have been fiddled with, they could run faster, slower, or anything.
I agree that one can get fooled by over-emphasizing light speed constancy. The definition of speed depends on the way time is measured. In fact the modification of Maxwell's equations I proposed predicts variable light speed, when the wave equation is solved. I did not want to get into that, since a recent paper of mine in Physics Essays does so.
I completely buy the mass-energy equivalence as physics. It is the logical link to the LT that I question. But, as I said, we are in danger of merely reiterating our positions. Remember, "time" in the LT is always proper time. Deviate from that and it is a new ballgame.
GPS time or CT, as I choose to see it, requires a "Master Clock" showing its proper time, at rest in any inertial system. ("Slave" clocks in other states of motion are corrected to run in step with this Master.) That could include your CMB system, but does not require it.
Best, Tom