I fail to understand how switching from a digital thermostat to a mechanical one would make an HVAC system suddenly work better. I would think that a new digital thermostat would have fixed the problem too. I have a Honeywell WI-FI thermostat, but I only installed it because I got it free from my electric utility. Yes, they will control my thermostat on peak usage days, but I can override it. I already had the radio control system that would shut off the outdoor unit on peak days.

I used to stay in a log cabin at a Boy Scout camp that did not regulate the heat properly. The temperature would swing up to five degrees. It had a mechanical thermostat with a spring, but no mercury. I was tempted to get an inexpensive digital thermostat and replace the thermostat to see if that fixed the issue. The furnace was newer and a volunteer HVAC serviced it once a year so it stayed in good shape.