This reminds me of Mirroring a read-only mailing list in Discourse, but without the mailing list part.
Maybe running the site in read-only mode or development mode on your network is the way to go?
Also if you only need to sift through post content and don’t need the Discourse UI, a simple Discourse Data Explorer query can let you download a csv/json file with the data that you can use other applications to search.