Full disclosure first, I have never headed NE out of Snow Creek before, so I am just going by what my map says and my trips up Snow Creek. It looks to be 10.4 miles from the base of Snow Creek to May lake, however don't forget the 2.5 or so miles from the backpackers campground to the base of Snow Creek, so you are looking at 12-13 miles. The climb up Snow Creek is a good climb which will bring you to 6700' quickly, and from there it looks to be a steady climb to May Lake which is 9360'. So it is still a ways up even though it is spread out over a distance. Is it possible, sure, certainly if my wife is in the lead, but it would be a serious day.
I have stared at my map for a half hour now trying to come up with some good ideas I think I have a suggestion. It is has allot in common with Dave's trip, but it is just a little more challenging. First, the map that I have used for years and it is a great reference is from
www.tomharrisonmaps.com and it is:
Yosemite High Country pub. 2009, scale 1:63,360 80 ft contours $9.95
I would suggest getting yourself a good map like this one and then you can sit and daydream, I mean study, the routes to make an educated decision. You can get most all of this online I am sure, but you will want to carry a map with you anyway, and this is a nice waterproof map. Make the other six buy it for you, that is the reward for being the brains of the operation.
Ok, I am assuming that you are starting early/you are staying the night before in the valley; and not driving from Modesto or something crazy. The basic trip would be up 4 mile trail to Glacier Point and stay night one in Illiouette Canyon. Then day two head over past LYV and setup base camp. Day three would be a loop around and over Clouds Rest. Then day four would be up HD and then down and out. One downside of this route is you will be in some of the more popular portions of the park, so you won't be too alone, but there is a reason this area is popular.
Day 1:
7.0 miles. Up 4 mile trail to Glacier Point and then down to Illiouette Canyon for the night. The total miles is from the bus stop at Yosemite Lodge. I really like 4 mile trail, it is as always a serious climb out of the valley, but it has a nice steady grade and it is well shaded in the AM. You get great views of the western end of the valley for most of the climb and then at the top you come around and get the eastern view. Did I mention that you are across from Yosemite Falls the entire time. (Not that it will be any kind of falls in Aug). Then you have an easy couple of miles down to Illiouette Creek for the night. Illiouette Creek is a beautiful area.
Day 2:
7.9 miles. Head to Nevada Falls around the Panorama Cliffs. From there I would go past LYV and setup a base camp along the JMT past the HD trail seperation. This will get you out of LYV and far enough off of the HD trail to get you out of the traffic. I have never stayed in LYV myself, I have heard about all the bears there and people and I have just avoided it. I have stayed just a few miles out many times and have never had any critter problems. Just my prefference.
Day 3:
9.3 miles. Head up the JMT along Sunrise Creek and then split off north to the Clouds Rest trail. This will take you up Clouds Rest approaching from the north (my favorite approach) and then the Clouds Rest trail will bring you right back down to your camp. This will be a fairly good climbing day, but with lighter packs you should make good time.
Day 4:
12.0 miles. From your base camp head up to the top of HD. Get an early start and avoid all the people coming up from the valley. Then come down, pick up camp and head down to the valley via the JMT or Mist trail. The mileage is pretty high for day 4 but it is allot of down along the Merced. If you want to shorten up day 4, you could pick up camp on day 3 and camp along the HD trail close to the tree line. This would add to 3 and subtract from 4. As usual everything is adjustable.
As I said before, these are popular areas, but you won't be walking in a line of people all day, other than in the Mist/JMT corridor. Staying a few miles from LYV will quiet things down some as well. Clouds Rest is my favorite place along the rim of the valley, so I wouldn't miss that one, myself.
I hope this doesn't add too much more to the confusion.
R.J.