[Brian in Tucson]

I am predicting it's not the oil cooler.

I would have the poor thing towed to a shop and have the coolant system pressure tested. My gut feeling is that you have a cracked head, when the engine gets hot, the pressurized coolant is being pushed into the oil galleys and ends up in the crankcase. Which is why your coolant goes down and your motor oil goes up.

It doesn't look like you have that much oil in your coolant tank, when the coolant cools it's probably sucking a little oil into the cooling system.