To get up to the Zoo would be a pretty big hill to climb, but you could take MAX to the Zoo, then follow the original posted route along 26 (there is a path that is not on the highway). Here is a link for yet another option from the west end of the Sunset path to PCC. There are no bike lanes on West Union, but I live right along there and ride portions of it almost every day with no problems.
I should also mention that the portion of the route that is just past the Sunset Shopping center on the map leads to a ped overpass that goes over 26 to the Sunset Transit center. You have to go down through the parking structure to get to the road that leads down to Barnes. If you were taking MAX to get to the Zoo anyway, you could just as easily stay on it until Sunset Transit (the next WB stop after the Zoo) and start biking from there.