Nobody said it would be easy.
A good start would be redirecting your energy from anonymously criticizing the leadership on public message boards. Beyond that, to do anything effectively will require leadership and initiative of your own.
Assuming you are willing to work with the present leadership (about whom I know nothing), your primary task will be to garner the support of the rank and file. When I say support, I mean practical support, not just expressions of support. The way to do this is through education and more importantly: visibility.
Does your domicile have a base rep? If so, that is the first place to turn. If not, guess what? Your domicile needs a rep. Either get with the current rep, if there is one, or you be the rep. Establish a communications portal where the pilots in your base have someone available 24/7 to address any kind of issue that may arise in which union representation may be required. Advice regarding grievances will be the most common issue, followed by Pro Standards.
Build a team. Encourage others to be part of the base rep team and advertise your services loudly. It may take some time, but eventually the pilots in the base will come to realize that you and your team are advocating for them. Word will get around that you are involved and effective. When that starts to happen you will find that support of the rank and file will follow, leading to a stronger union (in the true sense of the word).
Establish and maintain communication with the other base reps, to the same end as described in the paragraph above. Stay abreast of trends in what is occurring not just in your domicile, but in all the domiciles. Coordinate activities, always striving to be available and visible to the rank and file. Advertise (but don't embellish) your accomplishments at every opportunity.
Make no mistake, however: This will require a huge investment in time and energy. If your heart is not in it you will not succeed.
If this is more than you wish to take on, generally the communication and hospitality committees are always looking for help. Or there may be a committee in search of a chairman. If you have latent aggression, get with whoever is planning the strike (if and when). There is a lot of direct and hands-on work that needs willing hands and strong backs there. In these positions as well, strive for high success and high visibility among the rank and file. Point to the successes of the committee and your individual satisfaction in contributing to that success as you recruit others to join you.
If you are bound and determined to unseat either the Bargaining Agent or the EXCO, there are mechanisms in place and there are others who share your views.
Changing the Bargaining Agent is accomplished through the NMB. Their website contains all you need to know regarding the procedure. Be very careful if this is the path you choose. There is the dreaded "Seditious Weasel" clause in the Bylaws and Constitution of which others have run afoul in the past.
It has never been tested, only threatened, but either be very clear regarding your vulnerabilities here or be very discrete in the execution.
Your group can campaign for a recall of the EXCO. That procedure should be in the Bylaws.
The stupidest thing you can do is to go into either of these without a team in place that is ready to step in immediately with a plan that can be executed immediately. If you find yourselves saying "Yay! We won! Now what?" you will have failed before you began.
The least effective thing you can do (as in not effective at all) is complain in public under an assumed name.