I couldn't go up or directly out a wall, so I went down inside the wall between the studs with a 3.25x10 duct through the floor under the house and out the foundation wall. Not optimal size or distance but works ok with a 600 cfm hood.

Thanks scole250,

it's a log house so going through the walls is not an option. There are ceiling fans and lots of windows (there is a sun room a couple of feet away as well where the walls are nothing but opening windows) so the air can really move when the downdraft isn't up to the job (it's not great but it does part of the job).

Actually while writing this response it occurs to me the house smells wonderful (curry) and the RH at the stove is 25% (cold outside and there's a fire in the wood stove) so maybe we don't need a solution. No solution is an option I never considered...until now.