As always, thanks to all those more experienced than I, I appreciate the advice. I will go to rigid metal duct, straight outside. Now another question about noise and how to mitigate it. What is (are) the major sources of noise? - Is the noise primarily from the motor right down the duct through the insert into the room? In which case I can't think of anything other than something like a fantech silencer which will fit, but forces me into 2 more elbows than I'd have with a direct out. Maybe two additional elbows with rigid duct is a worthwhile tradeoff to incorporate a silencer? - Is the noise from the motor through the wall of the house into the plywood box and then into the room, in which case should I consider filling all gaps in the outside and inside wall with foam or some sound absorbtive material, pack insulation around the duct where it comes in through the outside wall? - Is the noise due to vibration? Would you consider vibration isolation between the external blower and the sheething on the outside of the house? Would you consider sound absorbtive material inside the plywood box to absorb sound there? Thanks...

OK, the facts restrict me to the Zepher Typhoon. A 'baffle' hood is too tall, and so will infringe on my workspace. The Typhoon is therefore the only product that fits the space and is not too expensive (Thermador) . The Typhoon as a tapered design (might be the wrong word) as it is 7" tall in the back, but only 5" tall at the front (the business end). So, 33" (top of stove to bottom of cabinet) minus 5" (Hight of Zepher) = 28" of space between bottom of hood to top of stove. Whereas the KOBE, as I understand it, is 10" tall, and would restrict me to a mere 23" of space from the top of the hood to the stove top. So that is it- done deal, getting the Zepher Typhoon as that product exclusively fits my facts. There does not appear to be anything alarming or plainly wrong with it. 850 CFM, at or about $1,000 Canadian. Self cleaning (kind of). No baffles, but this means no baffles that will surely tarnish, 'stainless' steel or not. The Thermador is $1,000 for the hood and then $1,000 for the blower (admittedly for a 1,000 CFM blower.) So the Zepher it is!

Here is a photo. Please excuse the mess. The duct snakes through and goes through an adjacent sidewall. That is behind that window. I don't think we do have the money and/or skills to redo the ductwork. This was supposed to be a minor renovation that turned into a fairly large expense. We bought an Ikea model and the hole to comnect the ductwork is up to that duct hole basically. The main piece is about 2 feet high. What I think I need is something with a slim profile like this undercabinet one: https://www.lowes.com/pd/GE-30-in-Convertible-Stainless-Steel-Undercabinet-Range-Hood-Common-30-in-Actual-29-875-in/1000180793 Would it be possible to mount one of these to the wall and not use a cabinet, and then just buy a separate duct cover?

Unfortunately that may be difficult to find. Most built in units are set up to be ducted. I saw a couple on Broan's website but they had ok reviews. They are not strong - the stronger units really are only the vented kind. Look into some of the big name brands - Broan, Best by broan, Vent-a-hood, Zephyr - I'm sure there are a few others. I don't know how fast you can get something like that - especially the way things are now, so you may have to wait. It's a shame there was no way to figure out how to get outside??