First, I'll answer Michelle's question: "why...migrate west to Washington State?"
Individual personal reasons can never be established. But, most went for free land for farming, ranching, timber, available through the Homestead Act (see below). My grandparents and grand uncle, came here for land for lumber. Others came for the fishing/seaport industry, many sailors from the Old Country, immigrated here and went to seaports for work. Others came for new opportunities in new towns and cities. Newsboys became publishers. Etc. Migrants always seemed to migrate for adventure, riches, land, family.
Now, for Tom. I see you've only posted 12 postings. When you post, it's important to provide the dates of birth of the people you seek if you have them. Identify if you've already researched the US Census, etc. It makes it easier for a volunteer researcher to find the "RIGHT" person. I did the 1910 Census so I could get the ages of your people. I did not find Jess in the 1900 Census. His land (see below) was in a remote area, and may not have been found in the 1900 census "IF" he was living in that area at the time. He wasn't found in NC.
I don't know what information you have on these people. Elizabeth Young "should" be on the Washington Death Index/Washington Death Certificate Index for 1903 to 1960...BUT, it can't be found on Ancestry or the Family Search indices. What happened to it over the past week? If you have the date of death and location of the "old Greene Ranch", you post it for further research.
The 1910 Census for Grouse, Asotin County, WA
Jesse R. Greene, age 60, born in North Carolina to both parents born in NC, farmer, owned his land, married 33 years.
Hellen A. age 56, born in NC to both parents born in NC, mother of 9/9 living
Clyde J, 26, (all children born in NC) not employed
Roscoe M, 24, teacher/public schools
Maude E, 22, teacher
Jesse H, 14.
The World War I Draft Registration Card Image Database:
Jesse Harlan Greene, born May 9, 1896 in Ingalls, NC.. He was a farmer working for J.R. Greene in Grouse, WA. He had military service as a private in the infantry for two years in the State of Washington. He was tall, medium in build, gray eyes. light colored hair.
---A family tree posted online by a MichaelWillis556, identifies Jesse R. Greene, born 10 Mar 1850 in Mitchell Co. NC, died 3 Dec 1937 in Inglewood, Los Angeles County, CA. No siblings identified. He married Helen Augusta Wiseman on 11 Nov 1877 in Bakersville, Mitchell Co, NC. She was born 12 Oct 1854, died 23 Feb 1953 in Seattle, King Co, WA. This tree only had children: Mary and Blanche, identified. Mary Delilah Greene, born 7 August 1880 in Spruce Pine, Mitchell Co, NC, died 21 April 1971 in Linville Falls, Burke Co, NC (no spoouse identified). Blanche Greene, born 1884, died in 1967, buried Cane Creek Cemetery at Hawk, Mitchell Co. NC.
---Another tree, posted by WilliamMcCarver, identifies Jesse Richardson Greene with the same data, also no siblings identified.
--Information from family trees MUST be verified by original documentation. A third family tree showed son Jess, but had the wrong birth data for his parents.
The Bureau of Land Management has an online database of land patents issued:http://www.glorecords.blm.gov/Logon/Logon_Form.asp
through the Homestead Act:http://www.legendsofamerica.com/ah-homestead.html
This database shows Jesse R. Greene obtaining 160 Acres on 10/12/1908. (J. Harlan Greene did so later. There was also a Columbus and Herbert Greene obtaining land in Asotin Co). This land was in Asotin County, Township 6-N(orth), Range 43-E(ast), Section 10 at the SE portion of the NE Quarter; the West half of the North West Quarter, and the NW corner of the SW Quarter.
--This "might" be the location of the "Old Greene Ranch" that you identified. If you do not know how to locate this farm land, I can show you how using plat maps on the Internet.