If you can fit it in at all, I want to put Daddy Long Legs on your radar. It's off-Broadway but it is the most beautiful, endearing show. I've just returned from seeing it the 2nd time, and I'm just in love with the show: the story, the music, just perfection.
I agree about what was said about Something Rotten and the tour option. The same applies for Curious Incident. It's a wonderful show, but absolutely not dependent on the cast. It will also likely run for a while longer, it's an open-ended run and still doing well. Not sure about the Fun Home cast, but Sydney Lucas (Young Allison) has already left. However, I hear her replacement is fantastic, and I don't think the show would lose much of its impact with different actors.
Most of the other musicals on your list haven't opened yet, so we can't really advice you yet. I wound however not recommend waiting for the official reviews to come out. If a show gets really good reviews discounts codes might go away (if you were planning on using those), and it might get harder to get good tickets - however non of those shows will sell out completely weeks in advance.
If you're looking for other play options, maybe look off-Broadway. Playbill has a good overview of upcoming Off-Broadway shows as well, and some shows are getting quite a bit of buzz already. The list doesn't have closing dates though, so double check that they are still scheduled to run in July, since plays are almost always limited runs.
Updated On: 2/7/16 at 11:14 PM