How to prevent the house from smelling of smoke after having a fire in the fireplace

Do NOT power-vent that room into living space. You never want to vent a room containing combustion devices into living spaces...as you state, that's asking for CO problems. It's not an issue of the furnace being defective, it's an issue of you sucking exhaust out of the normal path (the chimney) due to negative pressure.

You could get around this by using a direct vent/intake system where it becomes a completely closed circuit (furnace draws directly from outside).

I'm not an HVAC specialist, but a 90 degree room seems to me that there's something else amiss here...like maybe your circulating fan is underpowered?

Raising the flue may help a bit by increasing the draft. The direction of the smoke once it exits the chimney is totally dependent on the weather, winds and atmospheric pressure. You will notice that the smoke will go up when the atmospheric pressure is low, and will linger or drop in high pressure.

Raising the flue temp would require they open the damper and burn the wood more rigorously. This is often counter productive and sucks more heat out of the house than it puts in. Also in the case you site, a single wall metal flue could become extremely hot, especially close to the firebox. The smoke will exit the flue more vigorously, but not necessarily raise far enough before it cools to cure the problem.

Here in Maine where many folks heat with wood, the exhaust smoke is becoming an issue in more densely populated areas. There have been many stories on the news, and experts talking about new wood burning technology, but no one has found a way to reduce smoke pollution from older units, airtite stoves or folks that burn damp, or not fully dried wood.