I strongly suggest you implement some sort of monitoring on Twitter/Facebook/Reddit/TikTok et al. for your pseudo-anonymous domains. Either pro-active monitoring of "the firehouse" if available/affordable, or at least reactive monitoring of inbound referrers and unusually large traffic volumes to individual subdomains.
Please don't "just shut it down", fight it. At least try. We need more "good things" on the internet that don 't/can't get fucked up by people being assholes.
If your intention is "the domains aren't exactly meant to be shared on the internet for the entire world to pitch in ", maybe enforce that right up front? Ratelimit requests perhaps, so the first hundred or two requests are fast, but that it obviously and quickly slows down and becomes unusable above a certain size? Keep the free/anonymous service to a size that intentionally breaks well before it is involved in any (potentially problematic) viral social media stuff.
That might be a future path to monetisation even? Tweak your thresholds to it's fast and free for the first half a dozen or so people you share it with, but slows dramatically if you try and send a lot more people the link. Then you could offer paid plans with increased limits, you can then use the existence of a paying identity to avoid/block people who misuse the system? Even a nominal ~$5/year payment would dissuade griefers if you made it clear you'd supply payment identities to proper legal requests. And if your service proves wildly popular, selling "enterprise" account to to brands who want to use in in their viral content" attempts could perhaps not make you a unicorn, but could become a nice "lifestyle business". That'd spoil your HN cred, but "new Corolla every year" money from a side hustle is perhaps sometimes better that "swinging for the fences for dreams of Lambo money" gambles...