Best advice is to contact an immigration lawyer. I havent had any problems with adoption of out of status children. In most cases the judge doesnt inquire into the immigration status of the child at the adoption hearing.
The only challenge might be the termination of parent rights agreement, but a good lawyer can navigate through that.
As far as immigration is concerned, the challenge is the K-2 but its a minor obstacle, you can overcome that even if the child has to depart and re-enter.
This child is lucky to have you.
An adoption requires legal determinations in the domestic relations courts before immigration and a State Agency Governing child welfare can review the situation. Assuming that the courts take action and proper notice is given to the natural parents, adoption may be an options. How old is the child? Has the child reached 16 years of age? Some natural mothers, and the parents who adopt, are unaware that the natural child can no longer lawfully petition for the natural parents once they are adopted.
There are also challenges with adoptions that involve family members or natural parents whose actions suggest that they never gave up physical custody of the child. The facts suggest a clean break. You will need to find out how to carefully work with State of Washington Officials in charge of children and family services. It is unclear how soon you can be given legal custody, not simply constructive physical custody.
I suggest an appointment with an experienced adoption attorney who knows immigration law, as well, if possible. The adoption of a foreign born child in the U.S. can become challenging and costly, even if possible.
The above is general information and does not create an attorney-client relationship.