For Windows users, YogaDNS is a great little app for managing DNS configuration. Can set up DNS rules depending on domain name etc.
I actually use PiHole and added Local DNS entries for the archive.* domains in my PiHole config to fix the issue across my local network.
51.38.69.52 archive.is archive.today
41.77.143.21 archive.ph archive.li archive.vn archive.fo archive.md
And if all else fails, install Tor and access their site at archiveiya74codqgiixo33q62qlrqtkgmcitqx5u2oeqnmn5bpcbiyd.onion
I am on Google Fiber though, so I probably use 8.8.8.8 without explicitly meaning to. Perhaps this is a problem shared by both Cloudflare and Google's DNS proxies?
One trick that might help: I have found if I use a bookmarked page from archive.is, I can get to that. From there I can put in the original URL in the "Saved from" bar, and hit "Search", then I can usually get to an archive of the article.
Settings | Privacy & Security | DNS over HTTPS | Increased Protection | Choose Provider | NextDNS