...just updating this, for the folks playing along at home.
KoJ, FMX: yep, the old theromostat itself is fine. Opens in hot, closes when it cools back down.
I'd pressure test, but it's kind of obvious where the coolant is leaking; once it gets hot, it's venting right at the radiator cap.

On Civics, there's a small fluid reservoir off to the side of the radiator, and the boiling hot coolant is steaming out of that, as it vents into the reservoir.
What'cha guys thinking? Think the water pump has sh!t the bed?