That smell is typical with a gas range. You are supposed to run it with the vent hood on to prevent that.
Also, I've lived in several other places with gas ranges and never encountered that before. Maybe it was just worse with that range?
When I was remodeling our kitchen we went with a over range microwave because there really wasn't anywhere else to put it. Those are known for fairly poor airflow. We got a KitchenAid with some of the best available airflow, 440CFM IIRC, but stand alone hoods can do much better. I still have a todo of replacing the roof vent with a larger one, so there's probably still some restriction in there that's slowing us down. You might want to look for similar.