Looking for a nice coupe

Hi All-
I am looking for a nice XK coupe, 2012-14, under 40K miles, $35K or less.
There are a few on-line, but they have various red flags due to distance from Phoenix, service history, or obviously being rough even with low miles. My criteria are fairly narrow so this may not be a short search.
I’d obviously prefer a private-party sale vs. Uncle Joe’s Used Car Bonanza or similar sellers :).

Please PM me with any questions.