The east side is beautiful. I hghly recommend going counter clockwise and doing this section sooner rather than later, not just for the route finding (happy to share GPS tracks) but because the river crossings will be higher later in the day.
And it does look like permits are required 'Recreation permits are required in the Reservation area and are available for a small fee from administrative personnel in the area of Bird Creek Meadows.'
www.fs.usda.gov/recarea/giffordpinchot/recarea/?recid=79411
Ignorance is not a great excuse; we had climbing permits but didn't realize we needed a permit for circumnavigation. Duly informed and will do better next time. This site indicates you can also get the Yakima Reservation permit from the ranger office:
www.eyehike.com/Adams/Adams_Logistics.htm