First, I have to share my opinion of how to handle washboard roads.
It's all about speed. If you are just negotiating a stretch of washboard road between stints on the highway, and the washboard section has turns and can be run at speeds in excess of 30-35 mph, then I would NOT air down just for the washboard section.
40psi is a good pressure for your tires for onroad use. Your tires are not rated for road use below 35psi.
Often, going faster over washboard roads will yield a much smoother ride. It is a question of finding a balance between the tires/suspension and the frequency of the washboard bumps at different speeds. If the washboard bumps are consistently spaced, as is usually the case, by gradually increasing speed you will eventually find a sweet spot that will result in a relatively smooth ride.
If you feel you must air down for the washboards, then I would go no lower than 20psi and go no faster than 20-25mph. Even at that slow speed, I would slow down for curves and particularly large bumps/holes.
For rock crawling and more serious offroad use, your tires are certainly capable of being aired down to pressures much less than 20psi, but are limited to speeds much less than 20mph as well.
In summary, I would try varying your driving technique (speed) on the washboards before reducing tire pressure.