I think we can do something here. It is somewhat tricky cause we need to hoist out content and then re-insert it into the post.
I certainly consider this a bug, will put a pr-welcome on this for now, I may get to it, but it is a bit tricky. The server side needs to partially parse the markdown, remove the quotes, give to proofreader and then add them back in, this may end up resulting in the proofreader getting an incoherent thing to proof read.
Tricky problem.