One way to show tangible, useful support is to contribute money to "defend Monica from defamation by Stack Overflow":

https://www.gofundme.com/f/stop-stack-overflow-from-defaming-its-users

Monica has come to an agreement with SE and has stopped her fundraising.

Somewhat related is a fundraiser to literally pay respect to former SE employee Shog9 who was let go not too long ago, initiated by George Stocker. The community's reaction to his firing (as I assume) shows the hurt SE is willing to deal to the community for the ongoing course direction, presumably towards a larger, more profitable company.

The Monica Cellio affair was no isolated event.

UPDATE 2020-01-27

Monica has just posted this on Worldbuilding meta announcing that she is leaving the site for good, and highlighting further disturbing staffing developments. For the reasons I have outlined in the answer I wrote to Monica's post at the link above, I have decided that I can no longer contribute to the site. I am therefore updating this answer. I do not think the measures I previously suggested have helped: I do not feel SO has any interest in getting rid of the toxic atmosphere its actions have created. Therefore my recommendation is now that the best thing to do is to find another site for your Q&A activities. I plan to keep an eye on Codidact, hopefully the worldbuilding community will migrate there once the coding is complete, and hopefully you will all find suitable sites for your own Q&A activities. But I no longer recommend hoping that SO will "come good": this now feels very starkly like the slow-motion death of a set of communities.

The best way to help Monica and the site itself is not to let this issue drop until a satisfactory resolution is reached. Keep the discussion going on meta, keep the altered name tags supporting Monica if that's what you're doing, keep yourself marked as inactive if that's what you're doing. Keep sharing the link to the gofundme appeal. Perhaps those with suitable first hand knowledge should ensure that the Register story comments contain suitable accurate rebuttals and clarifications, to help in setting the record straight.

If the company hopes it can continue to more-or-less ignore the issue until people forget about it and move on, let's prove them wrong. For without a satisfactory resolution to something as vital to the site as processes for control of moderation, how can there be any trust, and without trust we may as well go and set up a work-alike site not controlled by this company and all migrate there, and nobody wants to have to reach that point.

You could publicise this interview with Monica Cellio on YouTube. The first 13 minutes or so are when she explains how the SE sites work. Then she tells her side of the story.

I was tempted to quote parts (because Monica so eloquently explains the situation). but I think it would do Monica a disservice. It's best to listen to the whole interview.

Personally, I thought her tone was objective and respectful. Her enthusiasm and optimism, despite all the events of the last month, shined through to me.

Here is an audio only version.

This may be a very bad idea that makes things worse, but as I did not yet see it mentioned, I'm just throwing it out there for consideration.

SE very clearly is actively ignoring the hundreds of topics protesting the decision. For whichever reason they seem to take zero action to correct this wrong. They can do this because Meta has no true reach within the network itself, and even less outside of it. All this concentrated outrage here has little to no public PR effect.

Yet we've learned multiple times that they are highly sensitive to feedback from outside the network, where a single Tweet can lead to immediate and drastic action.

Knowing this, why not play the same game? Take the story to the press. But this time told from the opposite side. A giant case file is already there. Make sure its something with reach and flashy, like Buzzfeed.

I have to put up some giant disclaimers here:

• If at all considered, it should be Monica's call to make as the outcome will affect her.
• I do not necessarily think it's a good idea, more like a desperate idea, I cannot really oversee the outcome and effects. A potential option when all other options are running out.
• It's not intended as an eye-for-an-eye action or activism. It is not intended to intentionally bring bad press to SE. Instead, the idea is to tell the full story as neutral as can be. A full story that was not told to the Register, as it was one-sided and fully controlled by corporate. Telling the community story is not bad press. It's just press. If SE prefers their conversations not here but in the press, well, let's have it?

Make sure at the next moderator election, candidates are aware of this case, so they know clearly the risks which are attended by a moderator's chair.

This may be foremost a good idea for helping others not to get into the line of fire of a press affair (at least if they don't want to). But I guess it could also help Monica, since the moderator exodus (and maybe future problems to restock moderator positions) is something I don't believe SE (Inc.) will completely ignore.

Without enough mods, the quality of certain sites will decrease. When quality decreases, the network will lose visitors, and when the network loses visitors, SE (Inc.) will lose revenue. So I guess if they do not want the next mod election to become a huge outrage, sooner or later SE (Inc.) will have to make a serious attempt to regain some trust, at least for their mods.

I think that What would be good "call to action" elements for "Reinstate Monica" profiles? lists the few "immediate low effort" things that users of the community can do: adapt their profiles, reach out into the public (for example by sharing links on FB, Twitter,...).

As already stated in the question, one can put the money where the talk is and contribute to Monica's GoFundMe campaign. You said it yourself, the key element is to reach out to as many people as possible.

Beyond that, I don't see much else. If you live in New York city, you might decide to do that real protest thing in front of their office building. Which would probably be a lonesome experience given that this is a global community, with not many members living in NYC. Of course, if you can turn such a protest into a media event, it might put plenty of real pressure on Stack Exchange Inc.!

In other words, our means are limited:

• we can strive to make "non meta" community members aware of the situation
• we can strive to create more public pressure

and that is about it. And unfortunately, in retrospective, nothing like that did have any visible effects.

We spread the news around, and we let everyone know what's happening

And we let SE realize how many people know what they did wrong.

I suggest editing the question to focus on the current phase of the Mess. (don't know what else to call it. Would welcome suggestions.)

By my reckoning, we are now in Phase III. Phase I was incredulity and very vocal outrage and an expectation that the onslaught of the peasants (us) carrying flaming torches up to Castle SE would cause the Powers That Be to reconsider and do something meaningful. Phase II was the realization that we had little effect. Phase III is now, with Monica taking legal advice.

And, by now, (almost) everything that can be said has been said several times. I'm sure someone can think of something new, but probably not much. Moreover, if we hope that Monica's legal strategy can prevail, we need to figure out how to let SE know that we are not going to go away, that our support is still strong, that we are not getting tired, but we shouldn't be inflammatory.

I don't know quite how to say this, but we need to have something like a cease-fire while still keeping the pressure on.

Most of the answers so far address this aspect (e.g., contributing to Monica's Fund, continuing with modified user names and modified profiles and proselytizing.) But, as for proselytizing, how? Perhaps a well-worded question on all the Meta sites?

Anyway, my suggestion is that the OP edit their question to incorporate some of these suggestions.

If you see an advertisement on an SE site, contact the company and ask if their advertisement means they support the slander of volunteers and/or the abuse of Creative Commons licensing.

Stack Overflow is doing me ongoing harm; it's time to fix it!

Was the retroactive change to CC BY-SA 4.0 approved by Stack Exchange's lawyers?