I can't really comment here about what I would do if I found Carson's strike. That might come back to haunt me in all kinds of ways.
I have a feeling more than a few people have been up to Twilight Creek head waters to search, and its possible its already been found. As has already been discussed, if a sheep herder found it, over the years any thin covering of dirt he placed over it would likely be washed away. I know people were living at the mouth of Twilight Creek on Lime for extended periods of time. In the old cabin I found boots, coffee cups, heavy metal framed cots, dishes, pots & pans, a cast iron stove in pieces, and even a lot of clothing. One shirt looked very new and was part of a Sherriff's uniform from Salt County Utah! Explain that one! So people were in a position to take day trips up Twilight, so it probably occurred. I also know 14er climbers have recently been up there as well. Who knows what has been found already, or maybe nothing. The oldest document in the cabin was a Readers Digest from 1952, and the oldest graffiti was from 1967. The newest graffiti was from 2011. So a lot of people found what I did. Food for thought.