You could gain entry into the 21st century carbon conscious global warming world and line the chimney and connect an epa burner on the bottom end. That's another way to eliminate the down-draft stench. Just throwing out ideas here .
Perhaps better than baking soda, or in addition to it, white vinegar works good for getting rid of odors, especially smoke odors.
Did the temperature go from being about 0 degrees to 60 over the same two days? Most likely a downdraft is the culprit.