Let's move on from the wood. A properly drafting fireplace can handle some smoky wood without it spilling into the house.
BigHappy534, did you already try opening a nearby window a bit to see if that made any difference? Does the house have an HRV or ERV for whole house ventilation?
Negative pressure is worth considering. The issue sounds similar to the OP. Both situations have an OAK connection to the fireplace. In the case of the original poster, they even tried pressurizing the OAK with a fan. In both of these cases, adding a smoke divertor at the top helped, albeit with a reduction of the fireview.Is anything running in your home that exhausts air to the outside? Dryer, range hood, bathroom fan, radon system, furnace, water heater etc? Maybe a negative draft issue…
BigHappy534, did you already try opening a nearby window a bit to see if that made any difference? Does the house have an HRV or ERV for whole house ventilation?