In my post #7 I attached a diagram which had the long run to the door chime C and asked you where the short circuit was. There is another wiring scheme which you may have though in which the long run is to the Nest Hello door push N; I have sketched this out and attached it.
Please would you study the two diagrams in #7 and here in #10; which is closest to your installation in terms of where the 'long run' heads to?
If your installation is more like the diagram here in #10 where was the the short circuit/repair done - at green or yellow? If it was more like #10 then you can see there is the possibility of causing damage to the transformer and the disc if the short was at the yellow point whereas only damage to the transformer at the green point.
The run that was repaired is at the green point. The wiring from the chime back to the door (yellow) didn't have to be repaired.
I need to do some homework and take voltage readings. I will also try removing the chime connector to see what happens. And maybe try reversing the wires (could reversed connections to the chime cause this problem???).
I'm busy this week with assorted things but am taking about two weeks of time off from work starting next week so I'll have time experiment then.
Thanks again.