Wikiquotes could be appropriate. Submitting a dump of the entire database to Archive.org could be appropriate. (For example, Archive.org hosts user-submitted dumps of things like product manuals, old TV shows, old computer games.)
[1] And even if submitting required licensing the contribution under some Wikimedia-friendly license, considering each person included in a quote would also have to agree to such a license... and I have a feeling bloodninja wasn't following up their conversations with "would you mind sending me a signed release of the above six (6) messages under a Creative Commons Attribution-ShareAlike license version 3.0?"
Edit: I think it'd be far better off on Wikipedia than Twitter
Mirrors still exist
(Also, Twitter already deleted old data, so these quotes wouldn't be much safer there)
My point is that the comment was praising independent services when it doesn't make sense: bash.org, the independent service, shutting down and people want to store backups in a more trustworthy centralized service, much like the two backups you linked.