OK, final results are in. I decided to check out etrailers.com as bigjim
suggested above. They were great! They listed 7 different hitches for the
Outback and I got the Hidden Hitch 2" Class III for $139.95, and the harness
for $34.95, no tax and free shipping. I got it in 2 days and it fits great.
It is recessed about 2 inches from the face of the bumper, just like I
wanted.
FYI the wiring connector is behind the side panel of the trunk, driver's
side. If you take out the foam piece on the floor(3 snaps) you can see a
loop of the wire hanging down under the bottom edge of the side panel. It
took me way longer than it should because I spent some time deciding whether
to pull out the side panel to see if that was really the right wire. I ended
up pulling the panel out and realized I could have just snaked that loop out
from under the panel. It is taped into a loop and the tape gives when you
pull on it. Don't laugh if everybody knows this but me. I didn't mind the
extra time since I didn't want to tear up the trim, but I could probably
have done the whole thing in an hour instead of 3 plus hours.
Thanks to bigjim.