To address this, I've calculated the frequency of days with measurable precipitation (≥0.01") by week (starting Jan 01, not smoothed) for the past 84 years:
By this definition, the climatologically wettest time of year is from mid-July through August, with a sharp drop-off in the frequency of measurable precipitation the first week in September. This is followed by a weak secondary maximum in late October. I'm speculating here, but I suspect that the sharp decline of damp days in early September is due to a decline in the climatological frequency of a big North Pacific ridge centered south of south of Alaska (which results in southwest flow aloft that brings moisture around the Alaska Range).