I have a burnham gas furnace (baseboard hot water heat) . Three zones each with Taco zone valves/heads. Three sepearate Honeywell thermostats. Problem occurred with only one zone. The upstairs was heating way past what thermostat was set at. Even after turning thermostat down all the way, temperature kept creeping up. ONce 80 degees hit at 4 am, we shut off furnace and gas.

In December we had the opposite problem with the same zone. There was no heat despite thermostat being up all the way. We changed the thermostat on the wall and put a new taco valve head on for that zone.
Serviceman said neither of those was the problem though. Technician said" pressure" was at zero, should have been at 20. He drained water from a valve and turned another valve to get the pressure up to 20.

Any suggestions as to what's wrong now? I'd like to have some idea before paying another service call. Thanks in advance.

So tech came in and raised pressure. Did you get heat after that? Or was problem never solved? Please clarify exactly were you are with heat right now. You may need to bleed a register, or you may have a bad zone valve(not just the head, but the internal ball).

If you were low on pressure, the pressure reducing vavle should be replaced. Im surprised that he would just up the pressure with a bypass valve and not fix the actuall problem with the auto feed vavle(pressure reducing vavle.)

After first servicing, heat came on and we had no further problems till yesterday.
Serviceman may have mentioned auto feed valve issue that could wait awhile (now that you mention it it rings a bell). I guess the time is now to replace.
What can we do to put the gas and furnace back on to get the two good zones back on heating and keep the faulty zone off for now?