Peter,
" If we change that oscillation rate (where emitted by what we call a 'clock') we do NOT measure a change in some mystical property called 'time', only a change in a local oscillation rate. That is the important difference missed."
I agree there is no mystical property called time.
"'Time' on the clocks of 3 people is co-ordinated and equal. But if one was approaching another at high speed the 'signals' from the other watch would simply be Doppler shifted, so the rate changed. We then need a new term 'apparent' time, which then defines SR's 'co-ordinate' time. But the rate of time (and watches) for all observers is unaltered. This very simple fact entirely eludes current theory and causes untold havoc and confusion."
The problem with this point is that the effect is not just doppler shift. Since nothing can exceed the speed of light, when you accelerate a clock and its observer to close to the speed of light, their internal atomic activity is in fact slowed, since the electrons are vibrating/cycling at nearly the speed of light to begin with, so when you combine both external velocity and internal activity, it still can't exceed C, so everything in that frame is slowed proportionally. I think though that this goes to the inherent inertial effect of space, rather than some spacetime geometry being a causal property. The fact is that the concept of time as part of this foundational math is simply based on measures of duration and how they are affected by context, such as velocity, gravity, acceleration.
Duration emerges from action. As you seem to agree in the first paragraph, time is simply the change caused by activity, such that if it goes faster, so does its "clock." Duration being what is physically happening between points of reference. So it is the slowed activity which results in slowed time, not time as the frame causing activity to slow.
So no time as mystical property, only measure of change caused by action.
Regards,
John M