This is not a situation where a tenant moved out at the conclusion of her tenancy and left property behind, as contemplated by the statute. This is a gratuitous bailment, where the homeowner agreed to store a friend's property for an unspecified period of time and now wants to end that arrangement. Even if we assume that the courts would view the friend as a tenant, which does not seem likely under the stated facts, we would be in a situation in which the landlord consented to store the property. In a bailment situation, the owner continues to hold ownership rights and is in constructive possession of the property.

When you're a gratuitous bailee, as a general rule, a gratuitous bailee is liable only for gross negligence that results in the loss of or damage to property in your possession. If you are later accused of conversion, a claim of abandonment can be offered as a defense. Given that the OP knew that her friend would be couch surfing, if it were me I would go beyond the terms of the landlord-tenant statute in terms of providing her notice of a date after which the property would be removed from the premises. Apparently there is continuing contact between Katie and the OP, such that notice can be given (and ideally documented) even if not mailed. Disposal of the goods presents something of a conundrum, as although I don't think the OP has a duty to follow the landlord-tenant statute under the facts, such a statute can by analogy reflect a reasonable set of steps to take, and the outright disposal of the property could be claimed to violate the duty of care. At the same time, there's a cost in removing the property to another location and for storage at that location. If there's no reason to incur that cost, the property can be kept where it is during the notice period.

On the whole the statutory framework for disposal of the property is probably one that can reasonably be followed, with the caveats that if I were trying to apply that framework to this type of situation I would take additional steps to ensure that notice were received (in addition to the mailing described in the statute), and I would not attempt to charge storage fees or make return of the property conditional on payment (as a gratuitous bailment cannot be unilaterally converted to a bailment for hire), and absent some need to remove it to another location I would leave the property where it is during the notice period to avoid incurring unnecessary cost.

It's also possible that, were you to discuss the situation with a Washington lawyer, the lawyer might suggest a different approach, as it's possible that we're being excessively cautious given how the local courts have responded to similar situations.