Get the proper and well-performing cfms on the hood you need, and add an HRV (heat recovery ventilator).

Look at Lifebreath or Honeywell

So, is the risk real or make believe? I mean, there must be hundreds of thousands if not millions of these 600+ CFM hoods installed, and few, even in new construction are installed correctly with make-up air.

I can't find any results for people dieing or being hospitalized for CO poisoning related to a hood.

I have a Viking range and hood, and we love them. My gas water heater and furnace are in an attached garage, and I live in a mild climate area, so my situation is different from yours,

BUT,

speaking simply from the hood's operating efficiency, you need to have make up air coming from somewhere for the hood to work. Air is stupid, it will come from wherever available - leaks in the house, down an exhaust vent from a gas appliances, etc. Unless you get the model with the remotely mounted motor, the thing gets so noisy that you will rarely use it at full power. We're normally at half, unless we're cooking many smelly things. In those instances, the fan is on high, a window is cracked, and you can't hear yourself think but the exhaust works great.

Stay away from the downdraft models - they don't work. I'm not saying they don't work as well, I'm saying they don't work. We had a friend get one based on a decorator's advice, we tried to talk them out of it, they now regret the decision.

Easiest solution - use it on low or medium for most uses, and crack a window for the brief instances when you need really good airflow because you're using many burners or you need to exhaust stinky smells.

Thanks snidely, I think your "Easiest solution" is likely going to be my solution. I will also make sure the wood burner flue is closed (until I get to removing it.)

It is real.

It is talked about a lot on the Kitchen forum.

The point (cfm) at which you need to provide MUA varies by jusidiction. Usually (but not always) around 400cfm.