I don't think there are electrical issues, but there MAY be some comfort issues down the line, I think.

Generally when your heating, you (the thermostat) might turn off the heater a little early and let the temperature drift up. There is then some amount of hysteresis in which nothing happens. I'm exagerating: Setpoint - 70. System turns on at 68, off at 70 and possibly drifts up a little to 71.

When in cooling mode , the system generally turns off faster.

You have to live with it and some babysitter will freak out that the "Heater is on in the summer". It's up to you.

I looked at some of the Zonefirst dampers and they are either a) Power open/power closed or power closed/normally open.

So you appear to have power open/power closed which is the hard one to deal with. I guess if the simple stat was a heat only stat, it makes sense.

Do that quick test and get back with the results.

Simple to fix on paper.

Operation of one stat:

Suppose a relay coil is connected to where cool belongs. This now activates an SPDT relay.

The HOT of a 24 V transformer would go to the common of the relay contact and the normally open contact would go to the side of the damper that would open the damper. The normally closed side would go the side of the damper that closes the damper. The common of the transformer would return to the Common side of the damper.

Now a cooling contact closure opens the damper and an open closes the damper.

Now connect the FAN terminal to the air handler and compressor and it works, but it isn't right either.

If you re-draw this circuit using a DPDT relay, the FAN terminal and the cool contact, you can get the Fan switch to just turn on the air handler, Cool to turn on the fan and the air handler and cool to open the damper. If you use the same transformer for the dampers and the AC system, then there is no danger that both dampers are closed and the AC and Fan are on.

I'd have to try to draw it.

I completed the schematic of how I think it should be wired as a .PDF file. This gave me sme encouragement to play with a PCB layout program. What's not shown is the operation of Fan/Auto which I will assume the state of that switch is an input to the thermostat.

When the stat is configured properly, a cool call will automatically result in a fan call. Anytime the fan is on, only the respective damper is open.

I hope you understand it.