My non-expert, likely useless, take on this:
Don't use Twitter's technology. If you're interested in quoting a tweet to create a public take a screenshot, copy of the text, quote it and provide a link. Simple.
If part of your post links, or portals, to another site you don't control it's not part of your blog/post/site. Complaining when remote content changes is pointless. You're not capturing what was when you link to remote content managed by someone else you're capturing something live, it's not a public record. It isn't quoting anything.