Layman said:
Even within the context of SRT this acceleration is "absolute," as I understand it.
Proper acceleration (i.e., felt acceleration) is invariant in SR, yes. You should really use that word instead of "absolute" to refer to such things.
Layman said:
really I've just been addressing, as SRT does, the comparison between two objects moving relative to each other at uniform speeds. I'm just saying that at least one of these has to be actually moving (whether you can detect which one it is, or not).
But how would you detect which one is "actually moving"? SR's answer is, the question has no meaning, because "actually moving" has no meaning; the only kind of motion SR recognizes is relative motion, since that's sufficient to account for all observations.
Your answer is, look to see how it got to the state it's in now. As you've been applying that criterion, it basically amounts to "look to see what Layman's intuition says about which object is actually moving". The only physical principle I can see that you've invoked is felt acceleration: look to see which object felt acceleration in the past. But that won't work even if we restrict to only considering objects that are currently moving inertially (so none of them feel weight). Here are a couple of counterexamples:
(1) Rocket A fires its engines and launches itself from the Earth. After a while it shuts off its engines and coasts. While it's doing that, Rocket B, which has been coasting towards the Earth, fires its engines and ends up on the same pad that Rocket A launched from. Both rockets felt acceleration in the past, so they both are "actually moving" by your criterion. But Rocket B is in the same state of motion that Rocket A was in before it launched, which according to you, is supposed to be "actually at rest". So is Rocket B "actually at rest" or "actually moving"?
(2) Rocket C is hovering high above the ground, firing its engines to maintain altitude. Then it stops its engines and starts falling. Is Rocket C "actually moving" after its engines stop? How does that square with the fact that firing its engines did not change its speed with respect to the Earth at all? (Note that in the other examples, mine and yours, rockets firing their engines *did* change their speed with respect to the Earth, which is what makes plausible the assertion that they are "actually moving" after they fire their engines.)
Layman said:
the question of how it came to attain it's current state of motion (and what energy is required to maintain that uniform speed) are relevant factors and considerations which it would be imprudent to ignore for the sake of absolute obedience to unproven postulates.
I have no idea what you're talking about here. Nobody has suggested that any of the things you mention about the train should be ignored. We're just saying that none of them amount to the train "actually moving", because that term has no meaning.
As for "unproven postulates", isn't that a tautology?