Pessimist in me says some kind of head issue as well. 240 is HOT. You could have had a very minor problem and then it started a feedback look of it affecting the cooling system, which made the engine get warmer, which caused the issue to get worse, which sped up the affect on the cooling system, which sped up the worsening of the issue, etc.
When the head gaskets went on my WRX a few years ago the symptoms were that it would get hot at idle (but would be ok while driving), and it was pushing coolant to the overflow and then not drawing any back when turned off. I noticed the problem starting when my heat wouldn't work at idle, system had lost enough that the heater core wasn't getting enough flow at idle. There was a small point in the gasket where combustion gasses were pushing into the coolant passages and then pushing coolant out of the system.
Sometimes, depending on the design of your cooling system, you can take the cap off and watch for bubbles while the car is running. I could in the WRX because it has a small tank right on top of the engine that is the highest point in the system. I could see a regular interval of bubbles when running the car at idle. They weren't fast or large, but it was consistent
Not saying 100% that you have a head issue, just that the symptoms as you describe could match that problem. .
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