The moon will rise at an azimuth of about 121 degrees that night -- well south of straight east. Therefore you might find that locations along the North Rim will give a better opportunity to catch the moonrise across the canyon, rather than through the trees. Along the South Rim, there might be a few overlooks along the East Rim Drive that jut out into the canyon enough to catch the moonrise along the edge of the South Rim, but it will be tight. Shoshone Point looks like the best bet. On the North Rim, Cape royal would be the natural spot, although other overlooks, such as Point Imperial might be good.
I've found that the Photographer's Ephemeris software make identifying and visualizing the locations of the sun an moon from any location very easy: http://stephentrainor.com/tools