From my perspective, stay with your fiance. Don't leave her behind. I've hiked Half Dome many times over the years. Its true that it is unlikely that someone will get lost. On the other hand it happens. There was a good example about a couple leaving the top of Whitney in the evening. She got ahead and went down the trail towards Crabtree Ranger Station instead of to Trail Camp and he went to Trail Camp. It took awhile for SAR to find her. Should not of happened, but did. Long time ago when I first tried Half Dome I underestimated my abilities. Went way to fast at the start and was tuckered out at the subdome. My girlfriend was just fine. Even though she wanted to summit and I said it was okay for her to do it she stayed with me and we turned around. Next year we summited together (she was still faster,but only by 5 minutes). It is a fantastic hike even if you don't summit. So just enjoy it.
Good luck!
