How tight is the house? It sounds to me there's no draft. Crack open a window and let some air flow in the house.
But I don't understand why the chimney is going from an 8" which is what's needed for a fireplace, to a 6" which is what's needed for a woodstove.
It's like having 3" exhaust pipes coming from your car engine and then halfway through the exhaust system, going down to 2 inch pipes. It's just doesn't work.
You're restricting the flow of the exiting gasses.

Sounds like a fireplace that was installed without any consideration to proper fireplace design. Many contractors just build these from gut feel, but there is much more technical consideration required. It all has calculations...firebox opening, flue size, chimmney height, direction of the roof, etc.

I agree totally with the last 2 posters, but I would like to add several other things that could possibly cause this problem. The chimney should be at least 2' above the peak of the roof. Sometimes nearby conifer trees can cause negative draft depending on which direction the wind is coming from. Does the stove have a catalytic combustor? Is it clean?? Hope this helps! PLEASE get back to us & let us know how you make out!

Jim