I have another idea (with no knowledge of how practical it might be to code/implement). Doesn't handle the copy & paste thing of course (I doubt anything automated could).
Standard quote functionality effectively copies the text of original post into the new reply and it therefore becomes part of that text (surrounded only by a wrapper to give it its formatting). Hence the need for separate editing to reflect the original contents, if the original changes.
Replace this behaviour completely.
When someone places a quote into their reply post ALL that gets included in their reply post is a cross-reference (such as quote=123456 - where 123456 is the post number of the post being quoted). When the reply post is displayed in the forum, the system replaces the X-ref with the then current contents of post 123456, presented in a suitable wrapper as now.
Upside: Would mean it was always up to date and/or reflect edits and deletions to the original
Downside: Would disallow partial quotes - replies to just part of a (perhaps long) post.
Therefore it wouldn't be ideal for all boards.