Hmmmm. The state code on involuntary dissolution for a non-profit seems to indicate that it may only take place when initiated by the state for failure to file the proper reports:
§ 24.06.290. Proceedings for involuntary dissolution -- Rights, duties, and remedies -- Penalties -- Fee set by rule
Failure of the corporation to file its annual report within the time required shall not derogate from the rights of its creditors, or prevent the corporation from being sued and from defending lawsuits, nor shall it release the corporation from any of the duties or liabilities of a corporation under law.
A corporation shall be dissolved by the secretary of state
upon the conditions prescribed in this section when the corporation:
(1) Has failed to file or complete its annual report within the time required by law;
(2) Has failed for thirty days to appoint or maintain a registered agent in this state; or
(3) Has failed for thirty days, after change of its registered agent or registered office, to file in the office of the secretary of state a statement of such change.
A corporation shall not be dissolved under this section unless the secretary of state has given the corporation not less than sixty days' notice of its delinquency or omission, by first-class mail, postage prepaid, addressed to the registered office, or, if there is no registered office, to the last known address of any officer or director as shown by the records of the secretary of state, and unless the corporation has failed to correct the omission or delinquency before expiration of the sixty-day period.
When a corporation has given cause for dissolution under this section, and has failed to correct the delinquency or omission as provided in this section, the secretary of state shall dissolve the corporation by issuing a certificate of involuntary dissolution containing a statement that the corporation has been dissolved and the date and reason for which it was dissolved. The original certificate of involuntary dissolution shall be filed in the records of the secretary of state, and a copy of the certificate shall forthwith be mailed to the corporation at its registered office or, if there is no registered office, to the last known address of the corporation or any officer, director, or incorporator of the corporation, as shown by the records of the secretary of state. Upon the filing of the certificate of involuntary dissolution, the existence of the corporation shall cease, except as otherwise provided in this chapter, and its name shall be available to and may be adopted by another corporation after the dissolution.
A corporation which has been dissolved by operation of this section may be reinstated within a period of three years following its dissolution if it completes and files a current annual report for the current reinstatement year or it appoints or maintains a registered agent, or files a required statement of change of registered agent or registered office and in addition pays the reinstatement fee as set by rule by the secretary of state, plus the full amount of all annual fees that would have been assessed for the years of administrative dissolution had the corporation been in active status, including the reinstatement year plus any penalties as established by rule by the secretary of state. If during the period of dissolution another person or corporation has reserved or adopted a corporate name which is identical or deceptively similar to the dissolved corporation's name, the dissolved corporation seeking reinstatement shall be required to adopt another name consistent with the requirements of this chapter and to amend its articles accordingly. When a corporation has been dissolved by operation of this section, remedies available to or against it shall survive in the manner provided by RCW 24.06.335 and thereafter the directors of the corporation shall hold title
to the property of the corporation as trustees for the benefit of its creditors and shareholders."""
It does not seem to that this would apply.
Assuming that you would be acting alone and could not get the board of directors to adopt a resolution to dissolve the corporation voluntarily, I believe that your remedy lies in filing a shareholder derivative claim. However, even in that claim you would not seek the dissolution of the company. Rather, you would seek an injunction ordering the company to follow the by-laws. You could potentially also assert personal liability against the directors for failing to follow the by-laws if there is some damage that you would be able to show.
I'm a bit uncomfortable on saying that this is the only answer. It's the only thing I saw in the statutes, but I'm going to opt out and allow another expert to pick up the question and see if they can give you a more confident answer on this subject.