One thing that I question, and I could be way off on this because I don't use a screen. By screen, I'm assuming a false bottom in the cooler tun? How much dead space is there? I'm just wondering if your grains are being saturated enough during the mash. I like to use at least 1.5 qts/lb in my mash. If a gallon of my mash water isn't even in contact with my grains, that ratio will be lowered significantly. It would even more detrimental to bigger beers.
Again, I could be miles off on this observation, but seems as though it should be considered.