@Debts_of_Despair and @sequoia
Thank you so much for your take. I hadn't considered asking our family mechanic to have a look. Would I ask the private seller to bring the car to my mechanic, and then have him look it over? That's a great idea, and it feels safer, too.
And I appreciate the feedback on the price. Fortunately, I'm not in a rush. I have the luxury of hunting for a really good deal.