I have precisely the same issue, but my transformer is a Nutone 10VA: a 16 volt 10 amp transformer. The voltmeter measures 17 volt output at the transformer and at the indoor chime. Without the "Chime Connector", which Nest help personnel seem to suggest is a surge protector, the chime works fine with the new Nest doorbell. Put the "chime connector" in the circuit, however, and I get nothing on the indoor chime. I have tried the "lengthen the chime duration" technique, and it does nothing, except that with the lengthened chime duration and no "chime connector" the indoor chime will hum for the period of lengthening and then fire.
During my last episode with Nest help (which seems staffed by generally inept individuals who read from scripts), I asked whether it was possible that there was a voltage issue. He seemed to be able to test voltage remotely and indicated that he read 14 volts, that he could not help me with that, and that I needed to hire a "professional installer." After hanging up I tested with a volt meter and read 17 volts. My chime is one of the most common chimes manufactured by the largest chime manufacturer (Broan-Nutone) and if this is inadequate voltage, then Google-Nest is guilty of false advertising. They are, at a minimum, guilty of making help unavailable (hold times over an hour) and providing not helpful help.
I was thinking of purchasing a new chime transformer but am uncertain it would resolve the issue and I cant get anyone from Nest to answer my question. Did you resolve your issue? Has anyone else had this issue? Is there an email address where intelligent humans answer help questions (the Nest people on Chat clearly do not).
