Thanks for the update.
As far as your chimney guy, he should certainly know there are more reasons for a chimney than venting smoke to the outside. The second less obvious reason, and the most important, is to create a low pressure area in a stove or fireplace feeding oxygen to the fire. The entire principal is about creating a pressure differential between inside and outside of the flue. The greater the pressure differential, the greater the draft. Lowering the indoor pressure with mechanical fans decreases the differential, or the pressure the air has to push into the stove. (or through your glass doors) When low pressure areas move over, you will notice a difference with less pressure pushing in. This is made up for by increasing the opening size of intake and adjusting damper for a hotter flue producing more draft to make up for less pressure at the intake. If he knows it or not, his job is all about very minute pressure changes inside and out. Wow.
Maybe you weren't aware of the basics, so knowing the principals helps diagnose most problems. There's not too many ways you can have unburned wood other than lack of oxygen or removing heat. No intake vents on doors or in fireplace and a lack of moving air up chimney caused by mechanical fans is the probable cause of smoldering out before burning completely. Giving it air into the fireplace behind doors will only cure the burning problem and give you a draft through the house towards the exhausting blower or appliance. It would prevent the air coming down chimney, but you don't want the cold air draft through the house toward the offending blower either. The intake into basement makes the furnace much happier, plus the radon fan isn't pulling heated air out of the house.
Is there somewhere else the radon blower, gas furnace, clothes dryer, bathroom fan, kitchen range fan, or any other blowers exhausting indoor air out of the building gets air from? Is that chimney the only opening from indoors to out? (most of these exhaust vents have flaps to prevent air leakage in)
Most fireplaces and chimneys didn't compete with all those exhausting appliances when built. Over the years as these new inventions are added on, the leaks and cracks into the building are no longer enough to supply the indoor air requirements. Caulking, vapor barriers and tighter windows and doors all add to the problem. The path of least resistance becomes the chimney.
If you close every window and turn on a few of these blowers and exhaust fans, try an incense stick or shake out a match in the fireplace and see which way the smoke goes. You may smell or feel a draft coming in, supplying the air for the building. You can Duplicate what happens at night by running the furnace, radon fan and any other automatic appliance that exhausts outdoors during the night. That will show just how much air is coming down the chimney with those items on during the smoke test.
Another test should be done at the gas furnace diverter if it is a natural drafting type furnace. (burners ignite heating combustion chamber that exhausts through a box with large opening into chimney to dilute and cool exhaust gasses) With furnace off, shake a match out at diverter intake to see if air flow is up chimney or being pulled back into house. This could be the intake the radon blower is using when furnace is off. When in use, that's two appliances pulling from another source, presumably the chimney.
There are ways to measure differences between indoor and outdoor air pressure. This is the weight of the air in the atmosphere at any given time at your elevation outside, compared to inside, while mechanical blowers exhaust. Similar to blood pressure using inches of mercury in a U shape tube, this measurement is in Pascals. -10 Pascals is enough negative pressure to experience all sorts of issues including fireplace smoke and smells.