Power off - XBee Explorer Board Regulated ?

Trying to get the most out of a battery operated remote control that uses an Xbee radio.
I have been able to sleep the Arduino Nano and I think the Xbee radio itself.

In my testing with a Uno board, at best I get down to 70mA of power consumption.
I read that the Uno uses 10mA just for the regulator, my regulated explorer board seems to be using about 40mA when I try it with no radio connected.

Can anyone suggest design ideas to reduce the explorer power consumption ?

Is there a way to "kill" power to the board (shutting down the radio completely) and then turning it back on when the Arduino wakes up from a button push ?

Thanks.