UN 13,768 is sequenced with Holy Cross Ridge (13,831) for an extra long dayhike with a lot of elevation gain. One way mileage and elevation gain are measured from the summit of Holy Cross Ridge. Round-trip mileagfe and elevation gain assume completion of the sequence and going over the summit of Mount of the Holy Cross.
From the summit of Holy Cross Ridge (13,831), continue following the ridge south for another mile to UN 13,768. You will lose about 450 in elevation to the saddle. The descent off HC Ridge went smoothly for us, but it is almost all entirely on broken rock and boulder-talus. The climb back up to UN 13,768 is not difficult, but consists entirely of the same boulder-talus. There is no rest for the wicked on this one. Though the elevation loss and gain is not significant or very steep, it is tedious because of the rock conditions.
Any possible sense of release when reaching this second summit (or third if you climbed Holy Cross), is squelched by the thought of having to retrace your route back over HC Ridge and Holy Cross itself. It will be more than tempting to do a contouring traverse to avoid the upclimb. Contouring on the west side below HC Ridge will take you over very large and not very stable boulders. Concentration is required for every step. The contouring traverse below Holy Cross is similar with very large boulders to manage. It will take even longer than the previous contour, before you reconnect with the Holy Cross north ridge trail. Then remember, you have an uphill section of hiking once you cross east Cross Creek to get back to Half Moon Pass. Ugh!
Another tempting possibility for a return route is to drop to the east somewhere. On GE, it appears that the least problematic return this way would be to walk along the ridge south from UN 13,768 to the next saddle and then drop east into a glacial cirque with some of the "Seven Sisters Lakes." Ice axe may prove handy in making the descent. There is an upper lake at 12,750 ft. and the next one down is about 12,300 ft. From the second lake you will need to hike back uphill to the east to connect with the Fall Creek Trail that will take you north over Fall Creek Pass and back to the Half Moon/Fall Creek TH for a total mileage once you connect with the trail of almost seven miles. We have not actually attempted this return route, so choose your poison.
A useful hint: One way to tackle the two ridge summits would be to turn this into an overnight, backpack trip. Pack in from the trailhead over Half Moon Pass and down into East Cross Creek. Camp in the vicinity of the creek overnight the first day. Do the climbs the next day and then pack back out. This may help a little, but we will also warn, when we did this in late June of 1994, we encountered the worst mosquitoes we have ever experienced in Colorado. Tim grew up on the swampy Texas Gulf Coast and says he's never experienced a worse barrage of ravenous mosquitoes!
Links to other information, routes & trip reports for this peak that may be helpful.