I have tried the format flash option, waiting the 30s and 2min as suggested before reflashing with esp8266basic - the behavior is the same. The flash works, but I'm not convinced the little bugger is actually doing anything afterwards.
Could this be a hardware thing with the amica board, or what would a good next step be in debugging this? I did double check that arduino can flash a sketch that connects to home wifi, so I'm reasonably convinced the hardware is functional.
Looking forward to trying the esp8266 basic!