I have a friend named Mike Giamellaro who is on Mountainbuzz occasionally.
Many years ago, perhaps 1999-2001 ish? He endeavored on the Three Waters Project, where he set off from Three Waters Mountain In the Wind River Range and ran to the ocean. He did this over three years, covering a different major watershed each year, the Wind down to the Missouri- Mississippi, the Snake- Columbia and the Green-Colorado. He started well above the Green River Lakes, I believe on the Jakey's Fork or the New Fork.
The link to his journeys, 3wp.org
is expired but I would imagine he'd be happy to share his findings with you.