What should we do when gutter screens don't seem right?

Our house is in a windy area and features a couple levels of metal shed roof. I know we should have screens on the gutters to keep the leaves and birds out. We hesitate because leaves are not our problem.

We clean our gutters twice a year and notice a lot of powdery silt in the bottom, which probably comes from the dust in the strong winds. Then, when it rains, all that dust goes to the gutters. We must hose out the gutters to force that silt to the downspout. So we need a gutter screen system for our metal roof that can be removed for this hosing. I have not run into a gutter screen system like this.

Meanwhile, I use a downspout screen to keep the birds from building nests directly over the downspout. (We've had to disconnect the downspout twice to release a bird.) The tiny holes in the downspout screens get clogged quickly (within 2 months) which inhibits the water from going into the downspout. And the gutters overflow. My options, so far, are to build gutter screens out of hardware cloth with bigger holes or to clean our gutters 4 times a year. But we'd like a better solution.