Well, when you think about it, what will the scope of the project really be? The ride structure itself isn't changing. Any new ride elements - presumably new flats inside the main show building, lighting, props, and the animatronics themselves - are practically plug and play (and are presumably being fabricated now.)
I'm assuming the rest of the work will just be paint, signage, and tackling some maintenance on the ride system itself. Say the attraction closes not long after Dinosaur, if not the same day or even before. It's not a huge list to check off by Memorial Day.
But knowing Disney, it'll probably be the standard mid-July opening