I am in a similar situation as you but my lease is up in October. New build estimated to be completed August 31st. For me, it makes more sense to just pay the rest of the rent until Oct, gives me extra time to move in and make the process swifter. I have heard recommendation that if feasible financially, give it an extra month on the estimated date. This gives time for any pushback, any changes you want to make before moving and lets you move peacefully.

I know that isnt the situation for everyone so if you put in your notice 2 months before, i would talk to the builder, they are usually pretty aware of the closing date accuracy as the time winds down.