We returned home late last night from a 10 day WDW stay. We were at AKL CL 5/30-6/1. Here's where the construction stood then: All 6th floor rooms are closed, but construction hasn't started. The only 5th floor rooms open are Kudu. The 5th floor lobby rooms, Ostrich Trail, Giraffe Trail and Zebra Trail rooms are all closed. 5th floor on Zebra Trail is completely blocked off and that's where the construction was on the days we were there. The day we were at the pool, we could hear lots of noise; not sure how bad it was in the rooms because we were on the 5th floor Kudu Trail (room 5241).
From my conversations with AKL CM's, they admit that when this construction first got underway, there was lots of confusion and some very unhappy guests. They feel they have a much better handle on things now and from what I saw, I have to agree. They are not booking to capacity, leaving rooms available should guests have a problem with their room and need to be moved.
Personally, I wouldn't hesitate to book AKL again - but I don't have any young children who need to nap (although my teenager wants to!!

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I believe as long as you are aware of the construction and the possibility that, during the day, you might hear noise - request a room "away from the construction" and you should be fine!