If it's $2.7K/pop, it's long past time to replace the thing. It can be very frustrating to replace an appliance that might run well if you just repaired it, but often, it's cheaper.

That said, my uneducated guess would be sediment in the water interfering with the sensor. A filter on the water might help. We once lived in a house that had the only water without a filter in an entire condo complex. We had constant problems with sediment. (Doubt the furnace/water heater was much like yours).

If you have city water that is generally good, sediment shouldn't be a problem unless you have mild rusting of older pipes. With well water, filtration can be key. That said, city water in Flint Michigan was terrible.

We had pressure issues in our boiler of the same model. It turned out the city water was at a much higher pressure than is standard. After our plumber installed a pressure reducing device where the water enters the house, the problem went away. is it possible the city water pressure is at the wrong level or fluctuates?

Could be as simple as the need to periodically clean the sensor. Here's a how-to video that might be helpful:

https://www.youtube.com/watch?v=H54Bt15oPOY