You never know with the Tonys they kinda make up the rules as they go along depending on the season, but I don't think this score could be considered "new" despite the changes.
I believe the rule is at least 40% of the music needs to be new. Given how much of the material is the same, and seeing as some of the new material interpolates pieces of what existed before, I think it would be hard (but not impossible) to crack that number.
It could end up going either way, but I suspect it won't be.
I doubt it will be-and don't think it should. I think part of my gripe is that it was indeed nominated the first time. In addition, score is both music and lyrics-changing the lyrics should not be enough. They kept a lot of the music itself. (I mean I have qualms with shows under the classics rule-like Hedwig last year-which were never on Broadway and never got a chance at best score or book-that irks me a bit.)
I don't think it will be considered or it should be considered as a new score, because the main tunes that the show is known for are still there, and it wouldn't make sense to nominate those again.
There are also songs that are considered "new" which were actually cut from the original Side Show. I would be VERY surprised if the truly new material is anywhere near 40%.