Trouble diagnosing problem

this really sounds like vapor lock. next time this happens open up the carb and see if there is any fuel in the bowls. if there is then possibly some debris in the carb. Make sure the fuel return line is actually hooked up. I have purchased cars in the past that has this capped off. Check to make sure the fuel lines are not hitting anything else that gets super heated. if the line is hooked up and no gas in the bowl, then its time to start opening up the lines and checking for a plug. You can shoot some air into the lines using an air compressor line to clear debris out of the lines.

Finally , I think you now know "why" the car was for sale. I would try to make the nice guy who sold you the car pay for anything that you need to do to get this right.