The Motorcraft thermostat is around $130 shipped. That is certainly at the top of my list for what the problem could be at this point. But I don't want to spend all that money until I'm more certain that it's that. So I'll see what the people at the radiator shop can offer about it tomorrow. Maybe they can scan it for me or do some sort of diagnostic.
I will mention to them what I've learned in this thread about thermostat problem, possible air in the system, etc.

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