Successful capture and containment is the purpose of a kitchen ventilation system; of which one component is the hood. Capture and containment are also processes. Capture is the process of getting the rising and expanding cooking plume into the hood; containment is the process of getting the plume past the baffles [or other filter] and ejecting it to the outdoors [usually]. Capture is mainly effected by having the hood overlap the plume at the height of the bottom of the hood. Some capture volume below the baffles may be helpful for averaging transitory fume collection (opening a pan cover), but the overlap is the most important part. Capture is very modestly aided by the blower flow rate (CFM) due to the rapid fall-off in blower air velocity away from the hood aperture. However, containment is all about getting the plume past the baffles instead of having it bounce off of the baffles and other sheet metal parts. Reflection of the plume would occur due to conservation of momentum if there were no air flow to aid containment. Once the plume and blower-induced air flow is above the baffles, (which should have collected some of the larger-sized end of the grease particle spectrum), the plume is extremely unlikely to escape back down. Volume above the baffles is mainly needed to straighten air flow for smooth transition into the ducting, to provide room for an internal blower, if used, and to equalize the flow rate across the baffle extent. Very narrow (top-to-bottom depth) hoods may not have uniform flow unless the filter is fairly restrictive (mesh filter, say). The volume above the baffles is not intended to be a reservoir for fumes. So, goals should be: (a) your best trade-off between performance (includes noise), aesthetics, and affordability, (b) hood entrance aperture overlapping the rising and expanding plume, (c) achieving an actual 90 CFM per square foot of hood entrance aperture (blower has to be rated higher than this), (d) providing a suitably sized duct to balance low restriction with a goal of achieving 1000 to 2000 ft/min duct air velocity, and (e) providing a path or paths for sufficient make-up air. There are additional details that may be gleaned from various past hood topics here. kas

I believe there are rear exhausting wall mounted hoods, but I can't give examples at the moment. If you use a roof blower, it would be relatively simple to block a top port and add a back port (with the help of a sheet metal shop). In any case, this extract from the Wolf Design Guide (available for download) may provide some insight into what may be available in any particular hood series. "Pro hoods accommodate a 10" (254) round duct. Low-profile hoods allow for an adjustable discharge. All other pro hoods are vertical discharge. For the 24" and 27 deep wall hoods, a horizontal discharge kit is available through an authorized Wolf dealer." Wolf is pretty accessible; that is, they answer the phone, and if you call them asking about details I imagine you could get some drawings showing the discharge apertures. I have no direct experience with other hood manufacturers. kas

A local metal fabricator on the seedy side of town who does fabrication for the restaurant industry can create the needed liner that protects the wood. You are in rarified territory, even on the seedy side of town. You will need to provide the design, or pay for someone with design experience to create the templates.

A range hood above the cooking zone will potentially be able to capture and contain (the two primary functions of kitchen ventilation) the rising and expanding cooking plumes. This is difficult to impossible for downdraft systems, which cannot compete with a meter per second of rising effluent resulting from cooking at the temperature of grease or oil vaporization. It is possible to have a wall construction that makes duct installation difficult, or which would cause the effluent to exit into a deck space, but nominally, going through a wall is basic. Going up and through an attic can have some advantages (at increased cost), but the wall is the default exit direction. What does kitchen ventilation have to do (first dozen pages or so): https://www.tagengineering.ca/wp-content/uploads/2015/02/KVSApplDesign_catalog.pdf What is suggested for residential kitchen ventilation (along with many many threads here): https://www.houzz.com/discussions/5161173/hood-faq#n=77 Try to plan to determine hood requirements (we can help) before determining candidate hoods.