If the shows you listed are the ones you're interested in seeing, then it's very likely that they will still be around in a month or two. I live so close to Broadway that I can go anytime of the year, but I tend to go in the summer or winter more often than other times of the year.
Early September (first week) can still be quite busy because of the end of summer season and tourists still lurking about and/or visiting around this time as it is cheaper than July or August. The rest of September and October are decent theatregoing months, but you shouldn't have a problem getting tickets and crowds aren't overwhelming.