Is there anywhere he didn't go.
I don't know about the inscription (there was a lot of wood stacked up against the facade when I was there), but 1809 seem too early a date for the church based on its physical appearance, imho. Its wooden roof did not look 200 years old to me. I'll have to have another look at my photos of it. I was there in around 1999.
I have never been able to look at any copies of Handes Amsorya - it seems to be a very obscure publication that no English-speaking libraries hold.
What about Keshik Kilise, which is a little to the north of Kayaburun. Has he been there too?