While I was thinking about something else, I added a back shield to our kitchen scale:

A pogo pin connected to the circuit common contacts the copper foil when the bottom cover is screwed down:

The shield prevents the buttons from responding to fingers on the bottom of the scale, so it no longer wakes up when I extract it from the under-cabinet shelf, and concentrates its attention on the buttons, so it no longer seems quite so willing to lock up due to mysterious influences.
With an absurd amount of rebuilding, this scale is becoming not a complete waste of free money.
The batteries soaked up 240 mA·hr of charge, which means the scale drew about 10 mA/day over the last three weeks. Given that the scale’s original 2032 lithium cells have a total capacity around 220 ma·hr for currents in the microamp range, expecting them to supply a current around 10 mA is was absurd.
“… not a complete waste of free money.”
Free money? You have a source of free money?!? Please share your source(s).
It’s the health plan kickback for talking to my doctor: scrip, not real money, for use in the Company Store.
So it’s not really free money, but produced this thing at no charge. To me,anyway.