I don't know if you looked at the actual image of the 1930 Census you quoted? J. Earl Moore, head, age 44, born in Kansas to father born in Ohio, mother in Indiana, merchant/bicycles.He owned his home at 1626 Jefferson St.He was first married at age 21. Katherine, age 51, born in Wisconsin to both parents born in Ireland.She was first married at age 19.
The 1920 Census for Portland, Multnomah Co, OR J. Earl Moore, age 34, born in Kansas to father born in US, mother in Indiana, proprietor/repair shop.He was a widower.Renting at 340 ? street.
The World War I Draft Registration Card Image Database shows him living at 353 N. 23rd, Portland, OR.He was employed as Motor Cycle & Auto Repair, same address, business for himself.His nearest relative was Mary Lula Moore.
I find a family tree posted on Ancestry.com owned by a "Lynda Coop" http://trees.ancestry.com/tree/9278750/person/-823364774?ssrc=http://trees.ancestry.com/tree/9278750/person/-823364774?ssrc= She shows J.Earl Moore, born July 1884 in Kansas, parents: I.B. Moore, born 1860, and Mary A. born 1862.She shows a 1900 Census.She also indicates he died in Kingman County.I don't know if this is a guess, or based on some fact.She shows his spouse, Alberta May Siefert, died 2001 in Springdale, Benton County, Arkansas. In another tree, owned by the above, she identifies Alberta May Siefert - Moore - Shepard was born 10 Oct 1888 in Kingman Co, Kansas, died 24 Sep 1976 in Springdale, Washington County, Arkansas.She identifies Alberta and J. Earl Moore had a daughter Edna Mae Moore, born 23 Jan 1910 in Kingman County, died 9 Oct 2001 in Springdale, WA County, Arkansas.Edna married John Napoleon Coop, so the tree owner is probably a grand-daughter; great-granddaughter to J. Earl Moore (IF the relationship is proven). --The 1910 Census was enumerated in April.I could not find any of the three in the 1910 census.But, I.B. and Mary are also not found. --It doesn't appear this person tracked J. Earl much after 1900.The person in Oregon is very likely the correct person based on birth place, DOB, and place of birth of parents.