I would not see any reason it would not work with your ceiling. If you do the math with standard 36" tall base cabinets, 30" off of the cooking surface that would leave 24" of room to work with. Most inserts are 12" tall so that would leave room to duct out the insert. It sounds like this is a small job and the cabinetmaker did not want to doo the job. I would call around and find someone that would take the job.

This has come up before in a somewhat similar situation (see link below). First question is what you want above the hood. If I read you correctly, you have upper cabinets on either side of the range, but no cabinet actually above the range. This is where I presume you will build your custom stucco enclosure. The reason this is important is because it determines how you will "back vent." What I think you mean is that you need to vent horizontally. The term back venting is often used to describe a vent that vents straight back, so that there is no ductwork at all above the hood itself. This is generally true for true undercabinet hoods that mount to the underside of a cabinet immediately above the range. If however you have nothing above, then you can use any hood liner that can vent up and then horizontally out. Essentially any custom hood liner can do this, using either a blower mounted in the hood, or if you want a quieter vent, then using a remote blower located on the external wall where your ductwork will exit your house. There are many sources for such liners. Monogram is not typically thought of as a "top performer" for ventilation. With the uncertainty over GE Appliances now, I'd be even less inclined to use them. Do search this forum: there is lots of great information on hood vent companies. Some of the companies that get positive feedback here include Vent A Hood, Prestige, Independent, Modern Aire, Wolf and Broan. Other misc thoughts: Do you have exactly 36'' to work with in width? If so, then you will need a hood liner that is even narrower than 36'' to fit inside your custom enclosure, which would be limited to 36''. In that case your vent size is even smaller, and even 36'' is marginal for ventilation performance, as the usual recommendation is at least 3'' wider on each side than your range. You might compensate at least partially by choosing a hood that is deeper than usual, as long as it doesn't bump anyone's head. And, if you truly have to use a hood vent that back vents without any ducting above the hood, look at the VAH SLH-6. Here is a link that might be useful: hood vent thread

Here are some general suggestions: Ideally, the hood aperture should encompass the rising and expanding effluent. Where not blocked by the back wall or side cabinets, the expansion angle is within 25 degrees of a vertical line over the pan edges. This expansion can be sketched and bump-out vs. height can be evaluated. If the hood size turns out to be impractically (or unaesthetically) deep, reserve the most noxious cooking for the back hobs. Ideally, the hood aperture should be high enough to not hit one's head on when bending over the stove, or blocking sight lines into pots, but not higher than necessary. A side view stick figure scale drawing helps here also. CFM have to be sufficient to remove the captured air from the hood plenum (containment). This requires an air velocity equal to the rising effluent velocity (3 ft/s) over an area that is roughly equal to the aperture area at the baffles. (Some slack here can be tolerated depending on the hood baffles' aerodynamic details.) (Hoods one can stand to be near without ear protection do not suck up effluent from the cook top.) Area (sq. ft.) times velocity (ft/s) times 60 s/min yields CFM. Fans need to have zero static pressure CFM higher than this value by some factor dependent on baffle loss, aperture losses, ducting losses, and fan curve factors. Plan on 1.2 to 1.3 to be safe. Various CFM rules of thumb (or nose) (or grease accumulation) may be found in various references. As an exercise for the student of ventilation you wish you had, read the references that may be found at my "clippings." Neglect not the issue of make up air. MUA is required in many jurisdictions when the CFM are greater than some value. This is a safety issue with combustion appliances. Search MUA on this forum for a second tranche of reading. kas

Thanks for replying! It is an interior wall that vents through the attic then roof. If I had to guess it's about 12 ft to the roof. There is existing ductwork to the roof but I don't know much about it. We did look outside on the roof and saw where the roof cap is. I'm sure that's not the right term for it, but it's a boxy looking thing where the range exhaust exits the roof (one story house). My contractor will do whatever is necessary to get this going. It looks like there is a rectangular box-like metal duct leading out from the range area into the wall. What happens up in the wall and attic, I'm not sure. The previous owner had a microwave with built in exhaust fan over a range in that spot. My contractor can duct straight up through the cabinets if need be. They will be ceiling height after crown molding is installed so you will not see anything. I do not do wok or high heat cooking. I sautee, boil etc, over the cooktop and use the oven. I cook every day. FWIW I am Italian LOL and growing up with the smell of food cooking was always a good thing :) I'm amazed at how many people think it's bad. Now the smell of burnt food and a smoked-out kitchen, that's bad! But I don't recall cooking anything on a daily basis that generates a lot of smoke over my current cooktop. I am currently, get this, UNVENTED, yes completely unvented in my condo. Cooktop is over an island. It's a large open floor plan, 10 foot ceilings, and in the 6 years in my current set up, no lingering smells and my ceiling is perfectly white :) Thanks so much for all of your help! Any advice you can give is much appreciated.