fantech.net sells blowers that do 600 CFM and less. It is possible for you to buy from a distributor who has a business relationship with fantech, but not from fantech directly. As luck would have it, the company that bill102 linked you to above is a fantech distributor, and can get the fan you want for your custom hood. Hope you understand that this solves all your problems.

You need to check the specs and make sure that all of the wood is covered by metal if you choose a smaller insert. I don't think the Broan you're talking about here will do that. It's a fire hazard otherwise. Choosing a wood hood is never a cheap choice. $1200 honestly is not a bad price at all for an insert with the capabilities that you need. Then there's the 2-3K for the wood surround. And the ducting, if it's not in place. And the electrical work, and the time intensive work of the cabinet installer to make it all work together. By the time you add up all of those additional costs that you're not thinking about here, that little bit of difference between something that might do the job, and something that will do the job is negligible. If you want to go cheaper, do a stainless chimney hood or an old fashioned under cabinet stainless steel hood.

Imperial makes hood inserts with a wide variety of options -- quality product, not cheap but not outrageous, either -- made in the US with a 7 year warranty. I own an Imperial under cabinet range hood with dual blowers and 8" round duct and have been happy with my purchase. Manufacturer is available to answer any questions, no matter how detailed. The front desk person knows their products, but if she's stumped, will put you through to their engineer. Also, can give you online seller I used, if interested.

The wrapping will help with vibration carried down the duct sheet metal, but not so much with acoustic noise carried down the air path. The silencer has to be larger than the duct for the same reason that a car muffler has to be larger than its exhaust and tail pipes. The acoustic waves have to be partially delayed to mix with out-of-phase waves to cancel some of the sound, without adding significant pressure loss. An alternative to the silencer for reducing blade tip turbulence is to operate the blower at a lower speed. For the same flow rate, this requires a blower that is larger in diameter than the usual manufacturer matches to desired flow rates. (Compare and or contrast a Casablanca type ceiling fan -- many CFM with no noise.) For kitchen ventilation, I would look into a commercial up-blast blower. These often have a belt drive between the fan part and the motor, and the belt sheave ratios can be changed for various purposes. So a, say, 2200 CFM rated blower operated with a sheaf ratio such that at full power the flow rate is actually only 1200 CFM, or whatever you need, should be considerably quieter than say a Broan 1200 CFM unit operated at full power. There are many up-blast blowers available from commercial ventilation distributors, but determining what you need may be difficult. It would be for me without getting the necessary literature. You may find a source such as Greenheck to be willing to provide some advice over the telephone or someone at a local commercial HVAC outfit. It is also possible (I've never looked into this) that Fantech could provide some low speed in-line blowers that together moved enough air and could be set to be lower in speed. This might be asked of their engineering support via telephone. But I would be surprised if they could do so without exceeding your duct diameter and still interface to the duct without pressure loss issues. Anyway, usually roof installations are easier to access than duct installations when the duct is nestled in the joist space and covered by gypsum.