Anaconda's installation does set all the paths properly, but the problem is using fish as the default shell. Because I'm not using bash as the default shell, I don't get access to any of the PATHs that are set by ~/.bash_profile!
One option would be to try manually setting all those environment variables in fish.config (or whatever it's called) but that seems like a pain.
Another option, from here, it to try this: "Keep your default shell as Bash and simply add the line exec fish to the appropriate Bash#Configuration files,"
I did that - adding exec fish to the end of ~/.bash_profile, and changed back to bash as the default shell. Now, when opening a new terminal window, fish opens and running which python finally gives me /Users/garylarson/anaconda/bin/python.