Apparently, as I have found out, the MCP1703 will leak current if voltage applied to the output gate and nothing on the input, while the MCP1700 does not. This is the case, when you power the Funky v2 from a CR2032 battery or couple AA batteries. Well, not so if you supply 3.3V (from a LTC3525 boost regulator), at which point the leakage is back.. So apparently this “breakdown” voltage is lower for a MCP1703 than a MCP1700 and this is why I had it all good under battery test. Apparently I am not the only one to walk this path, see this thread for some more detail.
So the solution to this would be to use the 3.0V version of the LTC3525 boost regulator instead of the 3.3V one. This also reduces further 25% in power usage when using the on-board boost regulator according to JCW’s article, so it may not be a bad idea at all. The only down-side would be if you require 3.3V for a specific sensor, but my experience shows that minimum voltage requirements are not so conservative and what works on 3.3V will most probably continue to work on 3V.