Down here for ventilation they remove the bottom boards and Varroa mit counting/sticky boards much of the summer for ventilation, but I have also been told by many that having solid bottom boards on gives the beetles more places to hide. Bottom oil pans are widely recommended for below the screened BB, for Varoa and the SHB. I have not heard anyone complain or mention that not having a solid bottom board has affected laying. I guess if it does, it is better than the beetles getting out of hand and sliming the whole hive :)
We were watching the Ohio Beekeeping series on pests last night, which is so old that it does not mention SHB. It said that wax moths are not _as much_ :) a problem in the north and north east as down south, because the winters do kill them out, and they have to migrate north each year, so it takes a couple more months for them to get far north, but that down here in the south, they can really get a standing population built up.
I hope for you that the SHB will not be able to survive the bitter cold winters up there, and population will at least cut down each year. They are said to fly up to 50 miles a night, so I can see how they spread every year. 10 nights is 500 miles...