How hard is it to fish a wire down the center part of the dash? I assume it's not possible without removing the dash from the front window?

When you say center of the dash are you referring to the center portion where the HVAC controls are?  Or are you wanting to fish a wire behind the dash the length of the dash?  If it's the latter, you can remove the glove box and lower kick panel on the driver's side to access things and route the wire.  It's not too bad.

I'm talking between the front windshield and where the air vents for the defrost vents are.

Like this

 

I don't know if you still need this, but your best option is to probably loosen the dash a little bit and pull it away from the window just enough to fish a wire through.  It's not extremely difficult to loosen the dash to move it slightly.  The pain is removing it completely from the car.

I ended up just sticking it on top of the center vent and cutting a little notch behind the plastic cover for the wire to fit behind.