Having deleted an entire story and reposted it, I'll state this emphatically: Do NOT post an old story as new! When I did, I immediately lost a third of my readers, who I've never regained. The story was better written, and it was a necessary step for me as a writer, but the story wasn't new, it was just cleaned up. As such, just repost the chapters and inform readers in the blog. Personally, I'd expect few readers will go back to investigate, but when readers go back to reread the story over time, they'll (hopefully) be impressed with the changes.
Also, don't discount readers who don't start a story until it's complete. Cleaning up earlier chapters is important to impress those readers. The people already reading your story are already impressed with your writing as it is, and those unimpressed won't be any more convinced to begin reading it when they see it appear again.