The article is from early June, so I'm sure that the renovations are much further along by now. In early June, floors 9, 10, 11, 12, and 14 were completed, and the work was being done on all of floor 8 and the south end of floor 7.
We were in a villa on floor 9 and never heard any construction noise, at least not that it bothered us.
We just stayed there 9/18-23 and it appeared that they were almost done. We had 2 rooms (standard view studio and lake view 2 bedroom) on the fifth floor that were both renovated. The only construction walls I saw were on the first floor north side just past the elevators. But by Friday when we left the wall had come down.
We were just there last weekend 9/17-9/19 and really didn't notice much construction at all. The only area we saw was on the sky bridge where you enter the Contemporary. If they were still working, we didn't notice it at BLT.