If you can’t bare to sale the car to a junk yard I would say you are an enthusiast.
For the problem to return in just 20,000 miles I would say your dealer did not fix the the problem properly. But I guess that’s water under the bridge.
Can you do your own work? If so you could give Allmeg auto parts a call
https://www.allmagautoparts.com/
and see if they have a motor. Then you can just move the accessories from your one engine to the new one. A JCW N14 motor is different than a normal N14.
Have you had the car checked for carbon in the intake?
It sounds like even if that was the cause it has bigger problems now.
How often did you change the oil?
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Thanks so much for your response. I was posting the thread out of desperation for a solution. I am not able to do the work myself and the
cost of a replacement engine and paying for it to be installed is just too much for the pocketbook to handle. I don't have a garage available
to store the car , so my options are pretty limited. If no one in the group has any interest I can only list it on craigslist.