As you can tell from this beefy-as-fuck wall of words, I've put some thought into this. It's big enough I'm going to have to split it in two. Hopefully there's some useful nuggets in here for the staff.
I say have a conditional DNP/DMCA system.
DNP for the art if it doesn't exist anywhere else other than a paywalled and/or self-hosted website of the artist to "respect artist rights" but require a DMCA for the art if it does exist literally anywhere else e.g. twitter, tumblr, derpi, furbooru, e621, pixiv, etc. Content that's up on sites that ignore takedowns e.g yiffparty probably shouldn't force people to use DMCA due to both ethics and optics, but that's your call.
For the details, require a moderate difficulty DNP e.g. require them to create an artist link code and put it on a public post from an artist account (and if you want to be smart about it, don't allow twitter accounts as valid artist accounts otherwise they'll virtue signal and rt the hell out of it). Of course, if the artist starts posting art again anywhere else to where the DNP wouldn't have been accepted, the DNP is considered reverted and any user will automatically be allowed to upload the content again, and the DNP will have to be re-established with the requirements of all other sources being removed again. If the artist requests a DNP with their content on non-pirate sites and says "that's not me, I don't control that tumblr/pixiv/derpi/messenger pigeon so it doesn't count" then too bad, if they care so much about not having their art up anywhere and they want the non-legally-required convenience of a DNP then they can either file a DMCA takedown for those sites first and then get the conditional DNP or they can file a DMCA here. If the code monkeys can swing it, a useful technical tool would be one or more of the following:
*Either allow registered users to go to an artist's DNP page and mark it as invalid by providing an archive link to a significant portion of offsite artist uploaded content which demonstrates the DNP is not being followed on all sites, which would (either automatically or upon moderator approval to prevent bad actors from creating drama depending on admin preference) mark the DNP as "DNP invalidated by artist" and link to the archive page(s) that invalidated it. You'd also probably have to list the date the DNP was created so older archives that have since been removed don't invalidate it.
*Alternatively, you could require a forum discussion in e.g. a pinned thread to have a mod manually alter the DNP on an artist page, and instead allow users to upload individual pieces of content from an artist that's marked as DNP by filling in an added upload field for the link(s) to the archive of the offsite image that invalides the DNP for that specific image. If desired, throw the "individual DNP invalidations" into a modqueue to prevent people from providing garbage archive links and allowing a bad actor to create a scandal on twitter. Until such a system is put in place, you'd probably have to set up a pinned thread for people to post invalidations either per artist or per image.
That should cover the majority of attempts of creating extra workload and devaluing the site by removing images for the sake of clout with twittermites.
This conditional DNP/DMCA system means that if the artist legitimately wants to have their art removed from the internet, or doesn't want their paid content leaked, then they can and people will have to go to a different site to get it. Those sites already exist so we don't need to take on those really bad optics right now, especially while trying to get established. On the other hand if the artist is just trying to clout around and is happy to have their art on other sites then they obviously don't have a problem with their art being on other sites, they just have a problem with this specific site; sucks for them because a DNP is a courtesy to those operating with good-faith, not a legal obligation we have to follow, so comrade checkmark will have to file a DMCA. This should discourage most artists from pulling their art for authoritarian good boy points. The price the site will pay (losing images from a few artists who actually go through with a DMCA due to the site "not respecting DNP", and a potential one or two who do it out of principle and wouldn't otherwise) will be far less than what we'd lose if we have a lax DNP policy, and the loss of art can be mitigated somewhat by third parties; the art will still exist in several other sites that already have the reputation for piracy. In exchange, the site (whose aim should be free speech and anti-censorship, not to pirate shit, two different things) doesn't gain a reputation for being a "criminal hub" like yiffparty is and anyone trying to discredit it as "not respecting artist rights" will have a hard time explaining why the artists in question haven't pulled the art from everywhere if they really don't want it being shared.
Finally, assuming people are vigilant about regularly pulling art from other sites, we don't have to worry about a few artists getting pissed that their art is on "the same site as the mean poner nahzis" and not uploading it themselves; since the new art people are importing from exists and is public there can't be a DNP on it, so their art is only removed in response to a legitimate DMCA request and still going to get pulled into the site as long as even a singe autist actually cares about it enough to run a userscript or point a downloader at a tag it has.