Okay, so I tried your method and measured the voltage across the circuit which comes to about 4.8V. Putting a 1M Ohmz resistor in series and measured the drop across it comes out to 4.1V. Did Ohmz law and got 4100 nanoAmps.
So I went back to reading your first question which was "Are other devices drawing power, eg. voltage regulators?". I looked at my board and yep, there a speaker pin and led pin that was drawing power which wasn't connected to the chip. I unplugged all of them and now it really is "bare-bone" (also disconnected the programmer) and re-measured the current and finally it's at 120 nanoAmps! Now I can continue to sketch E on your site.
Also, is it possible to wake the chip from sleep using a button press without using keypad2.h, but instead with a pin Interrupt function?