The question I think you want answered is this:
"What tire pressures for my rig should I use if I go off-road where I plan to travel under these circumstances"
1) estimated 100-200 mile trip
2) washboard roads
3) no sand/mud expected
I think the key to your last question is paramount: You plan to drive at 40-50MPH and only want to soften the ride somewhat, right? As you note, when tires are run for any length of time, the sidewall suffers. That is greatly increased by the speed at which you drive on them. In addition, since you are on washboard roads, not muddy tracks or sandy tracks, under inflation heat build up on the sidewalls is increased I believe when you go that fast.
Where I am going with this is just that I don't think you can have it both ways on what may be a washboard surface as opposed to a more forgiving on at those speeds.
The reality is you are going to get bounced around but you are trading a smooth ride for improper tire inflation based on the SPEED and the SURFACE of the road. Unless you plan on stopping many times on the journey where the tires could cool down, heat will build up and that isn't good for the tires.
Others have mentioned the risk of under inflation causing the tire to come off the bead/rim as well. Maybe it's just me, but I would approach what you have described at a much lower speed anyway. Furthermore, if some reduction in tire pressure is your goal to soften the ride why not try about five miles and see how it goes and if you wanted to, THAT is the time to reduce pressure by 10-15% to see if that helps. However, before I did that I would reduce my speed to 35-40 and see how the ride is then.
I know, its not an interstate highway so the ride should be expected to be not as smooth. You are trading SPEED for a comfortable RIDE at a possible cost of tire damage/potential dismounting.
Have you asked the mfger about running at that pressure on those tires and given them the conditions you outlined here?
Just sayin'......