John,
As Eckard validates, if you don't deny relativity you have to accept what the theory says about time.
"I'm not assuming any boundaries more substantial than a horizon line."
When you stand on the Maryland shore facing East, does Europe not exist at the same moment you are looking in that direction? Does the horizon which Europe lies behind rotate to meet you, so that you pleasantly find yourself in Paris if you stand still long enough? Only in a different inertial system, high above the shore -- could such a phenomenon happen for you. And even at that, you would have to invest energy in keep your vehicle in the same spot.
"With time as an effect of action, how do you draw solid boundaries between where a moving object was, is and will be?"
*Physically*? I wouldn't draw such boundaries. Time isn't an effect of action; time and action are related by very specific mathematical quantities of distance and duration, which is why the Minkowski space is a good choice to model dynamical and kinematic systems of events. If we wish to extend relativity, we don't wave a magic wand and say that we are going to preserve relativity, but do away with distance and duration. That doesn't work -- and can't.
I think, as I've said before, that brain science is the next big frontier of physics research. It is here, in the discrete relations among neurons in a connected network, that the quantum measurement problem really matters.
"Would you expect a measure of temperature, also another measure of action, to be infinitely precise?"
Isn't that what WMAP and its predecessors are all about? John, the reason that your ideas of time and temperature are unrelated to anything physical is that you think of temperature as something physically real -- while it is only a measure of averaged particle motion within arbitrary boundaries. The WMAP results assume the boundaries at the big bang and the present state of the universe. So our measure of temperature is at least as good as the accuracy of our probes, though never without boundary conditions.
Best,
Tom