Chris, First, is your father alive?Since you are asking these questions, I will have to assume he is not.Is your mother, or anyone in your mother's family that is still alive?If so, ask them.They always have clues.
Second, you have the adoption papers.Were the papers drawn and finalized in Washington State?Do the papers identify the Walter and Rose as birth parents?Or just persons that were providing the child for adoption.They could have been interested parties in the behalf of the child or the parent(s).Read the papers closely.Also, does the document provide the date of birth and place of birth of your father?
Now, this Walter would have been some 66 years of age at the birth of your father, not a major problem for a father, but the age of the mother would be important.
Next, you need a COMPETENT researcher in Grays Harbor to do secondary research.But, you must first read the adoption papers very closely for clues.A researcher in Grays Harbor could attempt to verify if this Walter was married to a Rose, could attempt to identify the age of Rose at the time of their marriage, or at the birth of your father.Next, trying to obtain his birth certificate is very important.That would/should identify the names of his parents.This Walter and Rose could be the parents of a woman that was your fathers mother, or may be local representatives of an adoption agency, or church.
Try a COMPETENT researcher in Grays Harbor via the Random Acts of Genealogical Kindness: http://www.raogk.org/washingt.htmhttp://www.raogk.org/washingt.htm The link is set to show Grays Harbor volunteers, BUT READ THE GUIDELINES FIRST.You can not email to more than one researcher at a time.Give them the information that you have, and find on the adoption papers and any information provided by family.