A fairly straight forward and painless way to access the Grunge Couloir of North Mount Timpanogos is via the NE Ridge.
To get to the NE Ridge, drive up American Fork Canyon to the Timpanokee campground, and enter loop B. Once in loop B (about 1/3 of the way around the loop) you will see a gate blocking an old road this is just before you cross the creek. Park at the gate, walk past the gate heading west, and watch for a single track trail on the right. If you miss the single track trail on the right, alternatively watch for a trail labeled 151 (Great Western Trail). The single track trail is a shortcut to the GWT (151). Follow 151 to a hamongong, this is the first meadow you will come to. At the hamongong turn left (west), and start climbing up the NE ridge (as outline in the picture above). You might be lucky enough to find game trails up the ridge. Gain the top of the ridge, and follow it to the base of the Grunge Couloir. Wooly Hole Cirque will be on your left (south).
Once at the couloir head up on the right side of the runnel. About 3/4s of the way up you will come to a Y, take the left branch and head up to the cliffs. Once at the cliffs traverse right (north) until you see the cornice. Look for a gap between the rock wall and the cornice, that is the key to exiting the couloir.
This image is attached to the Grunge Couloir