Using a coolant pressure testing tool determine if the system is maintaining pressure.
In 26 years my car never went over 230 regardless of conditions.
It usually operates in the 190-210 range.
Two or three years ago while in slow procession of 400 Vettes to the Ocean City NJ boardwalk, I was alarmed to observe a steadily climbing gauge confirmed by the digital as well.
When it went beyond 240 even with air on and revs up I really got nervous.
Was able to shut down when we finally got parked and was just below the real danger zone.
Driving home at high speed, I was able to maintain reasonable temp.
Every slow down caused a spike.
The cause?
The most minor leak around the lower hose. Minor enough that no drips were observed beneath the car, but enough to prevent the system from pressurizing.
Replaced with a screw clamp.
Problem solved.
Do not over pressurize it as you do not want to stress the heater core.
Worth a try.
Good luck and let us know.
Marty