I would like to send a HIGH signal down a pin to a switch and totally shut off power to my entire project.
It might have to be a LOW signal...
Use a MOSFET with a pull down resistor on the gate. The Arduino can put out a HIGH signal to keep itself alive then turn it LOW when it's finished.
To power it on you'll need to apply a HIGH signal to the gate until the Arduino can take over. You could add a button to the device which pulls the gate HIGH while you hold it down. This saves you from having to toggle the power switch.
The only problem is the default bootloader which will take a few seconds to start up (or maybe this would be a safety feature, I don't know...).
You can fix this by:
a) Using optiboot (the bootloader only waits three seconds after a reset, not after a power-on)
b) Remove the bootloader altogether (use an ISP programmer to program the board).