Personally I would first soak it in white vinegar for hours or over night removing much of the corrosion. Then while the rest is still softened up work on it with a toothpick.
Now this might make many cringe but what I have done on V nickels which I think get more stubbornly corroded than a buff is to take one of those fluffy and mildly abrasive wheels you can get for a dremel tool and clean up the surfaces. You can even begin to see a bit of silverish sheen. Put an old Covid 19 mask over your nose and mouth before doing this though.
I figure you're not going to hurt the coin value anyway as it's already enviormentally damaged. Just a couple of my ideas.
I have no grudge, because I did get the 1936 date from using glass polishing paper...a tumble on it really destroyed the detail. The date is even gone.