As noted for Dome Mountain, the official name for the trailhead here is "Boulder Gulch." Maps show that the main trail stays on the north side of the creek, however, Google Earth shows a slightly more visible trail on the south side as well. From the mine, we hiked along the trail on the north side of the creek. After a few hundred yards, the trail forks with one path leading down to the creek and the other climbing up just a little and then continuing to contour up valley above the creek. We stayed on this upper track for almost a mile before turning up the mountain on our right just after crossing a gully that was still harboring some snow. This is one of those narrow, entrenched gullies that originates high up on the mountainside. Coordinates for the place to turn up are: N 37° 52' 32.82" W 107° 36' 04.91", after crossing the gully.
Head WNW up the very grassy and steep mountainside. We had no trouble making upward progress, but the 1,800 feet of vertical gain along this steep route was relentless. Along the way, we saw plentiful evidence of elk in the area, but never actually saw one. Intersect the east ridge of Proposal Peak at about 12,700 ft. just where it turns to the northeast. Initial progress along the ridge is fairly easy, but the difficulties do increase. One section is particularly rocky with a rock tower to avoid (see photo) by traversing below it on the south side, and there is one cliff section to bypass closer to the summit where a north running couloir breaks through the ridge line. The summit is a moderately rocky affair, but it is no struggle to attain, other than continued dealing with the rocky conditions.
Enjoy the spectacular view of the north facing slopes of Tower Mtn. and Dome. This valley is short but beautiful. There was a fair amount of snow on the north facing slopes when we climbed this in late June - enough to afford a nice glissade if one were descending from Tower or Dome, but the route up on Proposal was not so fortuitous. For our descent, we took the south ridge off the summit for a short distance and then crossed over to a snowfield that gave us a quick descent into “Slagle Basin.” The first part is steep and then tapers out. Towards the bottom, the snow became soft as it played out in the basin. At a near level area in the upper basin there are a couple of exploratory digs.
Continue on down, descending steeply on grassy slopes and into some scattered trees on either side of the shallow drainage where you may be able to pick up a faint, old trail that switchbacks down to the creek. Aim for these coordinates on the stream, but you may not have to descend all the way down to find the trail: N 37° 52' 17.76" W 107° 36' 24.24". On the north side of the creek, pick up the very faint trail that leads back down the valley. After less than a half mile, it becomes more clear and soon, you should rejoin your original path back to the mine and trailhead. If all else fails, as mentioned before, it's fairly easy to cross the creek and pick up a more visible trail that shows on Google Earth on the other side.
Links to other information, routes & trip reports for this peak that may be helpful.