Particularly if it was the contractor's mistake on the ducting, I'd argue that you should ask for rectangular duct. We transitioned our 10'' round ductwork to 14 x 5'' rectangular duct to get through a second floor wall. Fits nicely between wall studs and provides almost the same cross sectional area as the 10'' round. The 7'' duct you have is just miserably undersized: a quick google search suggests that the max capacity you can expect is 400 cfm, not 600. No matter how large, or how many blowers you use, you really can't exceed the max flow rate allowed by the ductwork. 400 cfm is terrible--you're down into the OTR microwave hood territory. Totally inadequate for 85K BTU. It's only made worse by the long duct run you need. If you have any real hope of getting decent ventilation, you really should get creative and find a way to use larger ducting. As for the notion of two blowers, that also seems ridiculous to me, and the cost they are quoting you is highway robbery. Let's say you go with a single inline blower mounted in the basement. You choose a top of the line Fantech FKD 12XL fan, which can pull 2016 cfm with zero load, but more importantly can still pull 1066 cfm into a full 1'' static load. That should suffice for anything but a ridiculously long run. Of course you'd have to use a transition piece to hook to it (it's sized for 12'' duct) but that's easy. Installing the fan is simple: just hang it from a rafter, connect the duct and the power and you're good to go. You can buy an FKD 12XL online currently for $680. So the $2,000 seems way out of line. And BTW, the notion of using both an internal, and an external blower seems nuts too. You lose all the advantages of a remote blower by shoving one into the actual hood. But the bottom line is you really need to rethink the ductwork.

Between 460 and 600 cfms, it's better to have more cfms, and be able to run the hood on medium, than be forced to have the hood on high most of the time. Other questions to ask - do either of these hoods have baffle filters, or are the filters made of mesh? The Viking has baffle; the XO filters look odd to me though the description says baffle filters. Baffle filters are preferable because mesh filters can quickly clog with grease which impedes airflow. You have to be more diligent with cleaning mesh filters, though of course you have to clean baffles too, but not as frequently. The other question is the depth of these hoods front-to-back. Too shallow, and it won't cover the front burners, so you are paying for a hood that can't exhaust over the front burners which doesn't make any sense. Try to get a 24" depth if you can. If that is out of your price range, then settle for no less than 22". The XO is 22", and the Viking is 21" deep. The XO has a bad review on the ajmadison site. You asked whether Viking has better quality. Viking has had a poor reputation for quality for many years. They were good decades ago, not recently. The ajmadison site is very good because its search function drills down into details. I suggest you keep looking.

Thank you so much, kaseki,colbran, and weedmeister for your very helpful responses. Kaseki, the education you provided was phenomenal, and I really appreciate the time you took to explain the science behind the decisions. I had read the forums fairly extensively, but you have added new depth to the discussions. It is interesting - came home to read these responses after a 2 hour meeting with our contractor. One member of the team is urging me to get a hood that is 450 CFM and is dubious about the need for MUA. They also indicated that I didn't need the 36" hood for the 30" cooktop. (This is a very good company - considered to be one the best in town (I won't say where) and I know we don't have a commercial kitchen. On the other hand, we do use high heat to sear meats and to stir-fry. The person doing the construction diagrams did indicate that the information I presented and the questions I was asking were in fact consistent with safety standards (why you want a wider hood, MUA concerns etc). . It is an induction cooktop, which does reduce combustibles compared to our current gas stove, but I still want to make sure that we remove odors and smoke adequately. Because we live in a cold climate, we would need to address heating the air from MUA. From reading other forums, I get the sense that if I am running the a lower CFM hood at its highest setting, noise is likely to be greater than if I am running a more powerful unit at a lower setting. (Don't know if that's correct or just someone's opinion) I'll continue to read the sources you suggested to see if that is true. So far I can't find any dB information on spec sheets. Again, thanks to all of you for your responses.

Cannot answer your question unless you answer the following: What range or cooktop is the hood for? Is it gas or induction? How wide is it--30", 36", 48"? If it is gas, what are the btus. If you don't know that, then at least provide the model number of the range or cooktop so we can look it up. What is the size/diameter of your duct going from the hood to the outside? Setting all those questions aside, you should look for a hood that has baffle filters. The shape of it should be like a canopy shape. It should be deep enough front-to-back to be able to exhaust the front burners. Many cheap hoods are only 20" front-to-back, which is not sufficiently deep.