Your understanding is correct. There are three different laws of Washington State that are of interest:RCW 64.12.030
Injury to or removing trees, etc. — Damages.
Whenever any person shall cut down, girdle, or otherwise injure, or carry off any tree, including a Christmas tree as defined in *RCW 76.48.020, timber, or shrub on the land of another person, or on the street or highway in front of any person's house, city or town lot, or cultivated grounds, or on the commons or public grounds of any city or town, or on the street or highway in front thereof, without lawful authority, in an action by the person, city, or town against the person committing the trespasses or any of them, any judgment for the plaintiff shall be for treble the amount of damages claimed or assessed.RCW 64.12.040
Mitigating circumstances — Damages.
If upon trial of such action it shall appear that the trespass was casual or involuntary, or that the defendant had probable cause to believe that the land on which such trespass was committed was his or her own, or that of the person in whose service or by whose direction the act was done, or that such tree or timber was taken from uninclosed woodlands, for the purpose of repairing any public highway or bridge upon the land or adjoining it, judgment shall only be given for single damages.RCW 4.24.630
Liability for damage to land and property — Damages — Costs — Attorneys' fees — Exceptions.
(1) Every person who goes onto the land of another and who removes timber, crops, minerals, or other similar valuable property from the land, or wrongfully causes waste or injury to the land, or wrongfully injures personal property or improvements to real estate on the land, is liable to the injured party for treble the amount of the damages caused by the removal, waste, or injury. For purposes of this section, a person acts "wrongfully" if the person intentionally and unreasonably commits the act or acts while knowing, or having reason to know, that he or she lacks authorization to so act. Damages recoverable under this section include, but are not limited to, damages for the market value of the property removed or injured, and for injury to the land, including the costs of restoration. In addition, the person is liable for reimbursing the injured party for the party's reasonable costs, including but not limited to investigative costs and reasonable attorneys' fees and other litigation-related costs.
(2) This section does not apply in any case where liability for damages is provided under RCW 64.12.030, *79.01.756,79.01.760 , 79.40.070, or where there is immunity from liability under RCW 64.12.035.
So, an option you may want to consider is to get the estimates from the landscaping companies and obtain a real estate appraisal which shows the decline in value. You can then share that information with the neighbor, cite the relevant laws, and give a written demand for compensation with a deadline.
Alternatively, you can share those materials with a local general practice attorney who can write a "demand" letter for you to the neighbor. Again, if compensation is not negotiated or received by the deadline, then the attorney can file a lawsuit on your behalf and litigation can start.
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