"1) There is no volume of gas in the original high pressure tank - no single cc parcel of gas that does anything other than expand - whether it stays in the original tank or leaves the original tank. All the gas goes from an initial compressed state to a final more expanded state."
(I feel the hook in my mouth but, like a trout, I simply Cannot resist...)
I'm sticking with conceptual models, not math...Okay, let's look at that "empty" tank. It has no molecules of ANYTHING in it, so no kinetic energy in its content. Then that first molecule of gas arrives and, yippee, it carries with it some energy. Now a single gas molecule can't "expand" in that void...it can only bounce around inside the tank. It can't "speed up", because to do that would require energy and there is no place to get that. It's KE is already finite. However, what was once only "space" is now occupied by a single particle, so there is indeed a "pressure", though it's a very low one. Now here comes that second molecule. It's much like the first, but wait! Someone is already in the tank, so now the population of the tank is twice what it once was, so that first molecule registers that things are getting more crowded. Since it bounces off the newcomer once in a while, its movements are somewhat restricted. That makes it lose some KE...in the form of heat. It will do the same with EVERY ADDITIONAL molecule of gas that enters the tank, and the same will happen to each one of those, too. For that reason, the gas entering the tank is not EXPANDING into it. It is simply occupying the space, and every additional molecule of gas that enters compresses that gas, thus forcing it to give up energy that takes the form of heat.
Voila'.