Went to bed last night with the heater running & set at 72*. Woke up this morning with the heater still running and the thermostat reading 68*. Started checking the various registers, a couple had good airflow, some had very little. Strange thing is that one of the registers with good airflow is also the one that's furthest away from the unit. Put in another call to the original AC installer, I'll try describing the situation in different terms when he shows Monday.
I hadn't thought of the air loss through the chimney due to the fire/heat, and that having to be made up somehow. That may end up being another problem once we get the (likely) duct problem fixed. This old place isn't all that tight - it is tighter than it used to be - so there may be enough incoming through other leaks that it won't have to draw from the chimney. Although it may still draw from the chimney once the fire starts dying. Then again, there shouldn't be as much loss up the chimney once there's not as much heat... Then again, it'll most likely draw from the area with the least resistance, which may end up being the chimney.....
You still haven't (IMHO) adequately described your heating system. Start with the basics -- ignore the fireplace and chimney, as if there's no fire and the damper is closed. How does the heating system work? Unless it's a fairly modern system that continually exhausts a percentage of warm air and brings in a corresponding amount of fresh, outdoor air to avoid "sick building syndrome," it should be a closed system. All it's doing is pushing air through the ducts and registers from one part of the house to another. As such, it's balanced. A closed system is always balanced. You can change the amount of heat one room gets compared to another by opening and partially closing registers, but the overall system is just pushing air around inside a closed box.
Now you open the damper and light a fire. The fire needs air to burn, and the hot air from the fire goes up the chimney and is exhausted. That air has to be replaced. In leaky old houses, the replacement air sneaked in through cracks around doors and windows. The term for this is "infiltration." Because you're sending heated air up the chimney and replacing it with cold, outdoor air, it wastes energy. That's why the building codes changed to mandate glass doors and make-up air inlets for the firebox. That allows the fire to pull air from outdoors to use as combustion air rather than using the air you already paid to have heated by the furnace. By using glass doors to separate the firebox from the house, you allow (in theory) the house to remain a closed, balanced system while the fireplace and chimney operate as a separate, flow-though system.
The question is why your heating system isn't functioning as a closed system.