A respected collector once told me that dishwashers make an excellent job of cleaning mica shades. However, there was no woman in his house at the time.
Dishwasher may work but make sure all the water is gone before heating it up. Mica exists out of layers, the older it is the more water can creep between the layers.
I normally use a two day soak in Evaporust. I have also used 0000 steel wool and very carefully scrubbed the frame to avoid scratching/damaging the mica panels.