I think they've already started their next project, "The Battle Of/For Axanar" by filming some interviews with people during the Summer. And by "people" I mean friends who were more than happy to decry CBS/Paramount in front of a camera in return for a free lunch.
That will be the next thing they crowdfund for if they're legally permitted and, having read several comments from supporters, I think they'll probably get the money they need.
The analysis of settlement deadlock over this seems likely, if not the only point which may be in contention.
Settlements generally impose confidentiality precisely because the parties don't want all the revealed information to come back at them later.
It may not be legal for the studios to block a documentary, even if they get a ban over Axa-Trek otherwise. But they can impose such an onerous penalty and rip such a big one in Axanar's credibility in court that any documentary will seem like pointing to ashes blowing in the wind.
Its just amazing how deep a hole Axanar wants to dig for themselves in the name of ego, and how much pissedOffium explosives they want delivered onto them to help dig it. All indications are this project is not an innocent fan film, it is a professional, fully intentional attempt to build a commercial studio and collect numerous personal fringes off of very live IP owned by others, and then rinse and repeat indefinitely. There is no wiggle room with the law once this becomes clear in court.
Overall, my guess would be the studios are fine with this going to trial if necessary. The precedent of 'independent crowdfunded fan films' getting a free right to do what they please with entertainment IP needs to be contained. What better sort of case will come along to set a precedent than a law-defying, million-dollar-disappearing, hide-the-evidence producer who can't stand to shut up and let his attorneys make the case? Besides which, the rockslide is on its way down the hill, so you bet they are gonna aim it precisely.