I've noticed the same thing, though I don't generally go to the Theatre page unless I'm looking for a review. Usually, I just look at the three headlines under the Theater section on the main homepage - and they often leave the same stories and reviews up for days. With Isherwood no longer reviewing for them, the issue has gotten even worse, in that some higher profile shows don't get reviewed for a few days post opening.
The one thing I would say is that while Alexis Soloski may not be as well known as Brantley, she has been reviewing in New York for many years, has become a fairly regular third stringer for the Times, and also is the primary New York critic for The Guardian.
And I'm sorry if the thread on "Miss Saigon" caused any scar tissue, which was never my intention. As I wrote before, I appreciate that you posted the article, and I felt that an interesting conversation was sparked, in terms of how we are meant to regard the word yellowface.