Hopefully if there are any obstructions, they are just branches and so on. I'm patmac's husband. The chimney is the highest point around for more than 100 feet to the highest tree. The cap is brand new, with a baffle around it. I suspect the actual inside design of the fireplace itself may be the problem here.
Chimneys work by using the lift generated by the warm air column.
When that column goes down, something is very wrong with the house. Branches, firebox design, branches etc. Something in the house is sucking the smoke back down. In a leaky house, we often find hugh holes in the attic plane that allow huge volumes of house air to flow into the attic and out the vents. This air must be replaced and sometimes the easiest way for fresh air to come in is down the chimney.