Can you share with me which brand model that vent directly out? It is ok that it is week as long as it is 500cfm which is required in California. Thanks again.

All the models that I found were discontinued.and very tall. What they did in the picture above is a simple shell and mounted the hood blower on the roof. That's why it's so slim.

It's better to have the hood deeper, to capture steam and grease from the front burners. I used the 390cfm version of the insert in the following link, because it requires no make-up air. It vents from the top, but you can use an elbow to vent out the back--mine goes through space in the half-story eaves, then vents out the back wall, above the back porch roof.

Broan 500cfm insert on Amazon

How deep do you want the hood and what is your price range for an insert?

I have been researching purchasing an insert and having a custom hood made because I want a hood less than 20 inches deep but want a swooped design. If I had a gas range, I would put in a deeper hood. But I hate things in front of me as I cook and a shorter depth will work for my induction range's burner layout and my cooking preferences. I want baffle filters and Prestige, Zephyr, and Imperial offer lower height profiles with 12"-19" depths that I need; they also offer more choices for 24" deep models. Good luck!

I have found custom-making my hood and can lighting to be the most confusing choices I have made for my kitchen remodel...very limited local retailers (Ventahood only) and not a lot of detailed information resources on the internet unlike the wealth of info out there that made my other choices easier.

Make sure you spec to have that combustable wood trim high enough over the gas range. If you are going induction, the height can be lower. If you plan on a grill, I think it has to be higher than with just gas hobs and griddle.