Good timing :) You can first join the 4th Annual GGG meeting at Manzanita Point on Saturday and Sunday and then go on your hike on Monday and Tuesday. For a 20 mile loop from headquarter (or Manzanita Point) I would suggest to go down to China Hole, climb back up on the other side on The Narrows to Willow Ridge Trail and take that all the way to Coit Lake. From Coit Lake you can take Coit Rd to Kelly Lake. There would be your camp after roughly 10 miles. From Kelly Lake you can take Kelly Lake Trail until it joins with Coit Rd and continue to Mahoney Meadows Rd until it meets China Hole Trail which you take back to Manzanita Point.
The first 5 miles on the first day will have the most elevation change (roughly 1,100 ft down to China Hole and then roughly 1,300 ft up on the Willow Ridge Trail. The opposite (down over a longer stretch) is true for you second day. With all the little ups and downs inbetween you will most likely have some 5,000 ft of up and some 5,000 ft of down on those twenty miles. During last year's GGG meet in February we were not able to cross Coyote Creek at China Hole. It had become a raging river. This year we didn't get a lot of rain yet and right now I don't forsee any issues with crossing.
Have fun out there,