I had no idea you could ever see this from White Salmon. During COVID we rented a house there with an amazing river view and a kitchen to match. What a remarkable area!

This assumes air is able to flow in from outside of the house. Otherwise some air will be drawn out at first, and then the fan will just be maintaining a slight vacuum in the home.

And where does the floor vent get its air? Unless the answer is “outside”, you probably aren’t bringing enough replacement air into the home to allow for much air to leave.

You need lots of outside air to come in, and lots of room air to go out.

Consider that kitchen hoods are typically mounted within 30-36” above the cooking surface. They already have the advantage that hot air rises toward them, and run from hundreds of CFM to 1200 CFM or higher. A 6” duct is recommended for a 600 CFM fan. At 1200 CFM and above, 10” is minimum. And of course you need sufficient makeup air. Without that you’ve just created a negatively pressurized room full of still air.

You mentioned a duct supplying the room with makeup air. But again if you don’t have air entering the house you’re just negatively pressurizing the house without creating air flow.