According to a linked article, in one of the historical ones you posted, apricots take 3-4 days, in the sun, to dry. They’ll go brown without sulfuring, but that won’t hurt them.
According to Joanna White, who uses a dehydrator:
Preparation: wash, halve, remove pits and place on trays, cut side down.
Dehydrate: at 100 degrees F for approximately 60 hours, or until pliable with no pockets of moisture.
She mentions apricots are excellent for fruit leather. Puree, taste and add a little corn syrup or honey. Dry approximately 16-18 hours at 100 degrees F.
Even if the humidity here allowed natural drying, it would run into varmint thieving and the problem of ants getting into the food. I have a big stainless steel dehydrator which is used to dry food, make yogurt and sprout seeds when it’s cool. My guess is apricots do not like humidity and that’s why they don’t live for long here. Peaches, however, do great.