Interestingly simple fix. Do you think the original cap was a decoupler that just wasn't up to the job?

I think you are right. The battery power source is in the display, then there is a ~1m USB cable, likely cheap thin wire, to the scale. Having 100nF at the end of that may not be enough. They sell newer models that appear to be similar design (same scale and sliding box), but likely they've fixed this issue.