I'd like to add my (civil) 2 cents: TexasCatherder has a good question, and there are many right answers here. - Do you "need" a kitchen range vent? Yes, in most jurisdictions using international building code, some kind of kitchen ventilation is required. If you don't want it, don't put it in. But it may haunt you upon inspection at resale of the home. - No, few jurisdictions require a big ole' "range hood" over the range. In my community, it just needs to be some kind of vent that can circulate the right number of CFMs for the space. For example, a friend recently renovated her kitchen; she didn't want a big hood over her range in the island; and according to code, she went with a small wall-vent on the other side of the room on an exterior wall. That's enough for the "needs" of code. - But yes, like many have noted, a range hood does a better job of capturing grease and moisture than a wall vent. I'll bet my friend's lovely white kitchen wall gets a grimy film around that wall vent in a year or so. - Besides grease and water vapor, yes, gas-fueled heat sources produce toxins. It's not enough to kill or annoy most people, but the cumulative effects of the toxins isn't good, and those who are sensitive to allergies may suffer, and it's generally not a good idea to burn stuff (including chicken or toast) without ventilation. - Ventilation is important for indoor air quality and the structural integrity of the home. One thing that we recently became aware of is the need for ventilation just to get rid of moisture. If you have a well-sealed and insulated home, every-day water vapor from cooking, cleaning, bathrooms, laundry, etc. can build up and not escape the house. It can cause condensation inside walls and windows, which can lead to mold, which is a major indoor air quality issue in our part of the country. Additionally, although it doesn't seem logical at first, it can lead to structural problems. Air in a home circulates from colder regions to warmer regions, and the moist air goes with it. There's a photo in a an old-house-renovation book we have that shows rotting roof rafters in an attic: Rotting not from a leaky roof, but because of long-term water standing in a basement and crawl-space! It was three floors away -- how could that be? Air circulation moves the moisture up. - Anyhow, it sounds like our dear OP TexasCatherder got the point that ventilation is important. So maybe we can help her now focus on where to put it? Rather than debating the pros and cons of ventilation, perhaps we could start a new thread to help her with layout? She's going to have a beautiful kitchen, and folks here are great at taking the cook's priorities and giving suggestions for layout to help reach those goals.

Is there maybe a closet above that the duct can be run through a chase to the roof? You really need an on site HVAC specialist to explore all of the possibilities here. It may be that running the duct through the top shelf of the cabinets instead of in a soffit is how you have to handle it, but a pro might have other options after a site inspection.

Normally, the street sewer to which one's DWV plumbing is connected has a clear air path from under the street to the residence roof via the house DWV. Through this path, and the many others in the development, toxic and/or odoriferous gasses pass. The gasses are kept from the household air by water traps at the points of use. To have any chance that the gasses would not get into the kitchen hood and thence the kitchen when the hood system blower is off, a set of well sealed and powered dampers interconnected with the hood blower would be needed. I doubt even that would pass modern building codes, but it could function. Other houses' DWV would potentially be part of your venting system.

If you are going to do searing or wok type cooking, then the 90 CFM/sq.ft. value is what you want. But that is for actual flow. Multiply by 1.5 for the blower rating. E.g., 600 - 700 CFM for the 30-inch hood, proportionately larger for the 36-inch hood. If no hot oil cooking, then you could get by with using 60 CFM/sq. ft., and some of the lower rated hoods listed above might be suitable. Just keep in mind that whatever CFM they tout, the actual flow is likely to not exceed 2/3 of that value. I know that Beckett and likely the other burner manufacturers have MUA kits, and I would suggest they be used even without kitchen ventilation issues. However, you still need a source of air for the hood. This may be accomplished in many ways, but you have noted one of the easier ones; dump air into a mud room and heat it in the room. You may need more heat than you have now, but this can be provided by many different schemes and can just operate to keep the room at some temperature and not be linked into the hood controls. If the mud room has hydronic heating, either supplement it with electric heating, or be sure it is on its own zone and has enough heating capacity. (see chart) In considering hood designs (and I'm not going to rate those listed above), keep in mind that if you use a silencer (12 inches diameter on an 8-inch duct; 10-inches on 6-inch duct), the top of the hood has to be compatible with whatever enclosure you intend to use over the silencer. You may have to use a local sheet metal shop to fabricate what you need. The silencer requires the blower be downstream. Here is an image of a Broan blower that would typically be used on a sloped roof, but should be fine on an exterior wall. Wolf uses Broan for blower manufacture, I believe, so their external blowers should look similar. Abbaka (now part of Bluestar) also make such blowers. With an external blower, you can choose your hood for size and shape, and not care what blowers they might have squeezed in. Fan motor control compatibility needs to be checked.