My recommendation would be to send a letter to the person in charge of elections, Secretary of State for Washington. Include documentation of what happened. Request they confirm receipt of the letter and give you the name, address and phone number of the person who will sort this out.
Scroll to the bottom of the linked page for an address.
Apparently Washington state is happy with fraudulent elections.
It's just sad that this year I read through over 250 pages of information about ballot initiatives. That was a complete waste of my time.
I got an email back from Jacob Lodge who is Elections Supervisor for King County Elections, and he suggested using a different dropbox from the ones I've used in the past. I don't find that answer acceptable.
Include documentation of what happened with Mr. Lodge and with your ballot.
I would spend the money to send the letter requiring a signed receipt.
since that's the person whose desk the matter will end up on eventually.
How does Washington vote these days? Is it all by mail? Or is that just one option?
Definitely contact the SOS directly; they have processes to flag these to prevent this from happening.
They confirm I'm registered and have the right address.
I don't know how many thousands of votes were thrown in the trash this year, but two years ago they admitted on the news the day after the election that they threw away 7% of the votes. I don't understand why people stand for that.
They are supposed to have a specific reason for rejecting your ballot. You might try the ACLU, Public Citizen, etc. to see about doing something.
I used to work on Elections Systems... so in particular, if this occurred as you stated - all you had to do was go downtown to the Elections Office - and meet with them. The computer would call up your name and the other person (that shared the same information). They would validate the registration number that you have is different than the other person. In the event that have the same registration number, then an internal mistake was made. But they would also use information such as your address to ensure that no duplication of registration has taken place.
But go downtown and speak to them, they will address the issue...validation is by the registration number that you received.