Hmm, well good news – after one last stab it’s now working again.
I pulled the batteries, let it sit for long enough to make a cuppa, then tried the firmware update from within the app rather than by pressing the MM’s reset button. i.e. opened the (beta) app, observed the LOADING displays, pressed the settings button, then ‘Start firmware uploader’. The firmware flash process proceeded as documented from there (https://moosh.im/upgrading-mooshimeter-firmware/).