I'm thinking they will do 2 segments a night and cut them into the smaller segments. The big issue is rigging the load and bringing it to the ground gently. For these odd-shaped pieces, holding-on to them can be a challenge. hence they are making them smaller.
As for the supports, those are standard. They only push in one direction - up. Next time you see a concrete overpass going up, you will see the same thing. And if you look carefully at this picture of the construction of the hat, you will see that they used pretty much the same supports and locations to put it up. The only difference is that it went up in big sections - it wasn't covered in junk as it is now.