Headliner removal:
1) Remove A- and B-pillar garnishes. These just pop off.
2) Remove sun visors. The clippy-bit was tricky - you turn them and then they come out.
3) Unscrew lights.
4) Unpop the one clip in the rear of the headlinder, at the center, next to the hatch.
5) Headliner comes out.
The antenna base is held in place by a bolt, and has two wires running to it. As NoD~ has pointed out, it's powered. The washer nozzle clips into place, and I was actually able to get it off just by turning it and rocking it from the outside.
Bare roof:
The washer feed runs down the passenger B pillar:
From there it runs along the floor. I couldn't see where it went through the firewall but I was able to pull it through.
I tried NoD~'s stealth antenna in his suggested location, but found my reception wasn't very good here.
Radio reception seems like black magic to me. Moving it even slightly inside the car gave drastically better or worse reception. I settled on putting it behind the passenger A-pillar, where the old antenna cable (now removed) ran.
Antenna cable running along the passenger A pillar, and then behind the glove box to the radio:
Washer tube ends at the reservoir just in front of the front passenger tire. I was hoping to just unplug it and the pump would prevent fluid from leaking out, but I ended up needing to leave ~3 inches of tubing with a stainless steel bolt stuck in it.
The removed hardware:
Temporarily, I've stuck a piece of tape over the smaller hole and closed the bigger one with a carriage bolt, fender washer and neoprene gasket:
I rarely use AM or FM radio, and reception is no worse than with the original antenna removed and the base left in place, but I might poke around and see if there are any better (powered?) antennas I might use instead.