I'm no chemist, but it seems somehow the battery leakage affected the conductivity of some of the traces in the keyboard. Thankfully it was only a problem above the battery compartment, otherwise I would be better off finding a different keyboard that would fit. To fix the traces I had to take the keyboard down the rest of the way, which required cutting the places the membranes were bonded together, but it turned out ok.

I am neither a surgeon nor an artist, and MG Chemicals' silver conductive pen isn't exactly a precision instrument, but the traces work now. That's all I'm looking for in this thing. None of it will be visible anyways, and if the keyboard fails down the line, I'll either repair it again or replace it finally. For now, I have all 76 keys mapped out and ready for the next step. I'll put the matrix spreadsheet up in the files section once it's formatted properly.