^^^^^
That's life son. If you look at the city, and notice all of the buildings, they all had to rise at one point and made noise during their construction. The city was founded in 1624 so for 391 years, people have been dealing with noise as things rose.
The only plausible way I can see contruction not making noise is if they use legos. So its just one of those things that your going to have to deal with. Your in NYC. Your sensitive hearing surely notes the barrage of honking and sirens everyday, and so, this is just another addition to the festival of noises that one hears daily.
This is nothing compared to the noise at HY.
But at least shadows are not of concern with you. I think...