If you haven’t come across it, ThreadReaderApp does something similar to this but in a reverse syndication instead of the method you’re describing. It allows one to publish a thread on Twitter and then use ThreadReaderApp to roll the thread up and post a copy of it to one’s website that supports Micropub. I’ve written a bit about how it works here: https://boffosocko.com/2020/05/28/threadreaderapp-micropub-to-blog/
I’d love to see something more like what you’re describing.
Another interesting option for this that has a lot of the functionality you’re looking for is Kevin Marks’ http://www.noterlive.com/. I know he’s considered adding Micropub functionality to it. I suspect he’d be very open to anyone who’d like to add that or other refinements via pull request to https://github.com/kevinmarks/noterlive. It does post live threads to twitter and currently gives the output as raw HTML that one could cut/paste into their site.