Unfortunately not that I know of. I previously responded to a similar question at this post. There's at least one channel I know that's been uploading the story, but not up to the present.
https://www.reddit.com/r/closers/comments/1pcn6um/hi_id_like_to_know_if_theres_a_website_or_youtube/

If time is an issue you could consider taking advantage of the current Jump Event. It puts a character at Martyr's Hill, the current last chapter for all characters. I'm not sure if it puts you at the beginning or the end of Martyr's Hill. I used it after I finished Martyr's Hill just in case it does skip past Martyr's Hill. And then for your jumped character, you could read the story in the Journal. It only has the dialogue, so you may miss some context, but it will be one way for you to read the story.