Ah, I think maybe I wasn’t clear enough about our set-up…
The forum on Discourse is running alongside our main site. When a member visits the forum for the first time, it imports their username and profile pic from our main site. This is why, when they delete their profile from our site, their posts are not deleted from the forum. There’s just no longer a username or profile pic associated with them and the system automatically assigns this “anon” username retroactively to the posts.
You may have realised I’m not the techie here 
but I’ll look into these ideas. Thanks.