I believe the point that everyone is trying to make is that you cannot have different lease terms for single or married people due to the fact that marital status is protected by your state fair housing law. Marital status as defined by Washington State laws includes... Married, single, divorced, and widowed.
You are only requiring single applicants or tenants who wish to live together to sign your document. That is a violation of the law and could lead to a discrimination charge being filed.
Is your document worth the possibility of ten's of thousands of dollars defending it? You need a lawyer who specializes in your state fair housing requirements to confirm how this may jeopardize your bottom line.