I finally got the chance to take the last of the four Eastern routes to Hidden Valley.
Luckily for me, I was able to follow a hiker experienced in this route. I took some photos of landmarks that might help others find the trail, as it does fade in several places.
The first photo is more than half way up the ridge from the starting point, of a small window rock. The trail is pretty clear up to this point. The second photo is of a balanced rock, and the third shows what some have referred to as the large cactus just before the descent. I did go a bit further West, and went between the two very large boulders, but I could not find any cairns or evidence of a trail, so I went back to the cactus, and sure enough, just West of it is an easily descending trail into Hidden Valley (see the fourth picture). This is not the one I think shown in the main hike description, as I ended up just upstream of mushroom rock and the tunnel, not Fat Man's Pass. The fifth picture shows another small window rock seen from the Hidden Valley trail, and this is the location of where the trail from above merges with the Hidden Valley trail.
The guy who helped me find the trail descended to the South about 100 yards before the Saguaro, so now I have another trail to try out next time. Isn't that always the way?