Low powered wireless doorbell & door open/closed sensor
Why not have a reed-switch instead of a hall effect sensor?  These take no power and act like a perfectly normal switch.

And how about having the reed-switch / doorbell control the power to the unit?  You could arrange it so that when the button is pressed or the door is opened the power is then turned on.  The turning on of the power could trigger something else that turns on the power (such as a relay in parallel with the button) so the power latches on.

The device will then boot up and do what it needs to do.  After that it can then interrupt the power (turn off the relay?) and it all goes silent again.

You can't get a lower idle power than that now can you?