Here's how I successfully removed two corroded AA batteries from my Apple Bluetooth keyboard: Following others' suggestions I first tried baking powder, then vinegar, then WD-40 over a period of three or four days. What did the trick, I think, was several liberal applications of WD-40 followed by several soft blows to the "barrel" of the holder with a rubber mallet, then firmly tapping the open battery end against a kitchen counter padded with several newspaper sections. I did this more than a few times before the second battery fell out.
I gave the keyboard 36 hours or so to dry out, inserted fresh batteries and damned if it doesn't work. Maybe it'll work for you, too.