The battery is removed, and My MP-1 is powering up fine and retaining
settings. 

The picture is worth a thousand words. (Or, in this particular case,
8192 words of 8 bits each): 

Now I just have to just re-rack this thing, restore my presets which I
saved over MIDI, and resume shredding. 

Top left, you can see the desoldered battery, removed and lazily leaning
against a capacitor, having nothing to do any more. 

Bottom right is the daughterboard holding the new skinny chip, developed
according to a careful interpretation of the chip's data sheet, in
consideration of the ADA MP-1 schematics, and the data sheet of the
original TC5565 chip.