re: Thermostat help

Is your Nest powered by a common (C) wire? If not, perhaps you should hook one up - hopefully you have a common wire already there, not connected, you can use. Perhaps this article might help you trouble shoot assuming you have have not read it already LINK

FWIW, just passing this along, professional HVAC techs on the HVAC-Talk do not like Nest thermostats - they say they fix a fair number of problematic HVAC issues by simply replacing Nest thermostats. They like Honeywell and Ecobee smart thermostats. But that said the problem you are describing doesn’t sound like the problems they describe with Nest though I think I recall connecting a C wire helped to solve some Nest issues.

ETA: I linked one thread from HVAC-Talk where HVAC techs discuss issues with Nest thermostats relative a question that a homeowner had with a HVAC issue - you need to read 7 posts down where the issue with Nests come up. LINK