Thanks for all of the suggestions! I think the plan for now is to flush all the fluids and see what happens. I bought some cheap oil today for the first drain/fill cycle. Once I know the fluids are fresh and clean, I'll have a good baseline to work from.
I don't think I'm going to mess with the head right now. But I did bookmark the site for Time-Serts (just in case). But hopefully it won't come to that.
I have not seen any evidence of oil in the water, nor can I smell exhaust in it. The attached photo is what I mean by evidence of water in the oil.
The car had been abandoned for a year, but was not just ignored in a warehouse or something like that. It was at a repair shop and they occasionally had to move it around the parking lot. So it was started and run for a few minutes in order to move it. So the water I'm seeing could just be from condensation, as suggested. An oil change will tell me for sure.
I already planned to do a cooling system overhaul regardless. Given the age, mileage (140K), and unknown service history, that's a no-brainer. All that stuff needs to be replaced no matter what.