At an Indian store you can usually find ginger paste (I use ginger/garlic paste).

Yeah I feel that. I brew my own ginger beer so I generally use it all in that. Otherwise if you can use the canned minced ginger, while not as good as fresh, will stay good forever

But in this I just chopped it pretty roughly since it gets worked in pretty easily

freeze it! buy it whole, toss it in the freezer. you can grate it fine while it's still frozen and it keeps basically forever.

Iirc you can store tightly wrapped ginger in the freezer for, basically, ever.