I did the same as you did. Replaced sender; no change. Then replaced thermostat. Finally put on an accessory temp gauge which showed the engine was normal.
Yes, I was told it could be gauge cluster, lead wire, or sender. Anything shorting to ground that gives a low ohm reading to the gauge will cause the gauge to think it is seeing overheating.
But there's another possibility worth checking.
I don't know if your model has an engine computer. We had the same symptoms on our 2008 JD310. Even though I thought it was an old fashioned mechanical injection because of having separate injector lines (not common rail) and no emissions control....well, it turns out that our model did have an early version of an engine control computer.
That are a known trouble spot, and the temperature gauge falsely showing hot was a known symptom of failure of the early engine control computers. Our dealer had a replacement in stock and said they all do it sooner or later.....said to be worse in models with the engine computer mounted to the engine or frame next to the engine.
rScotty