My mother was from China from the Pearl River Delta region near Canton (not politically correct) and she was famous in town for her cooking abilities.
She would slice a piece of ginger about 1/8" thick and then smash it with the flat of the Chinese cleaver until it was pulverized and ready...
I use a microplane, as well, but instead of freezing, I use a plastic vacuum bag by Reynolds and pump the air out and the ginger keeps for a long time, won't mold nor dry out.
Jim