I have confirmed by suspicion that the on-board LDO voltage regulator is to blame for my troubles as described yesterday. I experienced the exact same situation with battery powered Funky v2 high sleep current as @Capnbry describes here, so I took his advice and swapped the MCP1703 with a MCP1700. It worked fine and now I get 0.072mA in sleep mode. It really beats me why it works, but it does. The problem is that the MCP1703 consumes current with voltage applied to the output gate and nothing on the input, while the MCP1700 does not.
I am glad this is sorted, although I don’t understand why it works 🙂