All Solid points - with only the smallest dash of sarcasm.
I’ll take a bunch of pictures in the next few weeks when I get back to the car, but your point on engine and system internals is the truth. If there is no documentation and/or trust of the seller your just gambling - and even if you get the car for a bargain a bad gamble can mean there is a series of payments laying just over the horizon.
I’m sufficiently scared off.