This would require buying an SSL certificate, which would cost some money but I'm not sure how much?
buying an SSL certificate, which would cost some money
Not necessarily, as Let's Encrypt is a thing.
IIRC Uncyclopedia (and other Uncyclomedia sites) uses Let's Encrypt, so maybe @Legoktm might be able to help out with the practical implementation (I'm guessing that the Let's Encrypt site itself is self-explanatory, but making Apache or nginx use the certificate and whatnot is beyond my skills).
I would recommend using the certbot utility: https://certbot.eff.org/ if this is your first time using Let's Encrypt. It has some more manual steps, but easier to understand IMO. And once you're more comfortable, you can use the simpler scripts like https://github.com/kuba/simp_le or https://github.com/diafygi/acme-tiny which require you to be a bit more familiar with SSL certs and stuff.
Also I would recommend using https://mozilla.github.io/server-side-tls/ssl-config-generator/ to generate your web server's configuration, and then use https://www.ssllabs.com/ssltest/ to test it and get to an A :)
SSL Certificates are not that expensive for what we'd need. Mutli-domain certificates are like $30/yr. Especially we rid ourselves of *.brickimedia.org domains and just make Brickipedia the only wiki on that domain we'd just need need two domains secured.