"It's 30% less duct run, but does that translate directly into 30% increase in hood efficiency?" The short answer is no, assuming "efficiency" meant "flow rate." The longer answer is that if the pressure losses in the ducting and from exiting the roof vent and from entering the hood aperture and from passing the hood filter are known as a function of flow rate, and the fan curve providing flow rate capability as a function of the pressure loss across the fan is available, then you can evaluate actual cfm as a function of how negative you will allow the house pressure to get. In other words, the duct losses are only a portion of the equation. They may dominate in some cases, but even then the fan curve must be known to make an evaluation. In the hope of making this clearer, assume that the abscissa of a graph is flow rate, and the ordinate is pressure drop across the fan. A conceptually idealized fan would be plotted as a straight vertical line at the fan's rated flow rate to some high pressure drop and then follow some monotonic curve to the ordinate where there is no flow rate. Alternatively, if a fan were to lose flow rate by 30% for 30% more pressure loss, the curve would be an inverse function (concave curve). Real fan curves are better than inverse functions, and better than straight-line functions between rated cfm and maximum pressure loss, but not square shaped. Hence, without the curve available, and some estimate of the other pressure losses, flow cannot be determined. (I once found example fan curves somewhere on Broan-NuTone's web site. They should provide some insight. Note that the curves will vary in shape with fan design.) kas

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You did great with the hard duct angle and foil tape. That’s exactly what needs to happen here. The hard duct needs to terminate into the roof cap and be sealed. You may need to remove that and create multiple sections to make that happen since the duct below has been fixed by you sealing it to your hood. A hood can not terminate inside the attic, which this one does, because it isn’t properly connected to the roof cap. A duct can’t use flex duct. The small aerosolized grease particles that escape the larger filter trap will accumulate in the ridges of flex duct. That creates a fire hazard.

I'm not sure I understand the intent of some of the comments. As I stated in the original post we blow hot air out of the upstairs windows while simultaneously opening all the downstairs windows to allow cool air to replace it. This method fills the house with cool air from the bottom up in the early morning when the outside air is coolest. I considered a whole house fan as we installed this in our last house and it worked quite well. Same principle - open all the windows downstairs while the fan blows the hot air out. I'm not sure how this got turned into an issue with not getting enough fresh air into our homes - we live in a mild climate and open windows to bring in fresh air all the time. This house has blown in insulation in the attic that is very light and is easily disturbed so I fear that an unducted whole-house fan would eventually cause the insulation to clog the attic vents. I suppose a ducted whole-house fan would work and I understand the reasoning behind separating functions. Since it seldom gets really hot we typically only do this for a small percentage of the days during the summer and it seemed to only have to run for about an hour so I thought it might be a good case for dual purpose. I just thought there might be some clever solution that could accomplish this without a lot of effort and expense. Thanks for the input so far.