Well, I'm a bit late on the update here, but it turns out that the car DIDN'T have any valve damage. The shop pulled the head, didn't see any damage, decided to consult their books, and discovered it was non-interference, like I was telling them. Turns out it was a dirty fuel injector keeping the engine from going..
To the shop's credit, they didn't just fix the injector, keeping our money. It's been an interesting trip, but we came to what I would call a fair deal. They basically waived all the labor, and gave us the new head gasket and antifreeze. They botched some aspects of the job, but they made good, so I'll be going back.
Moral of the story is that the Zetec is not an interference design.
Thanks for your support, all.