still confused enough to ask ... whether it's metaphysically possible for an object with a lot of molecular movement to be cold anyway.

Not so fast! That is possible, and that was EY's point here:

Suppose there was a glass of water, about which, initially, you knew only that its temperature was 72 degrees. Then, suddenly, Saint Laplace reveals to you the exact locations and velocities of all the atoms in the water. You now know perfectly the state of the water, so, by the information-theoretic definition of entropy, its entropy is zero. Does that make its thermodynamic entropy zero? Is the water colder, because we know more about it?

Ignoring quantumness for the moment, the answer is: Yes! Yes it is!

And then he gave the later example of the flywheel, which we see as cooler than a set of metal atoms with the same velocity profile but which is not constrained to move in a circle:

But the more important point: Suppose you've got an iron flywheel that's spinning very rapidly. That's definitely kinetic energy, so the average kinetic energy per molecule is high. Is it heat? That particular kinetic energy, of a spinning flywheel, doesn't look to you like heat, because you know how to extract most of it as useful work, and leave behind something colder (that is, with less mean kinetic energy per degree of freedom).