Just an FYI, so you know what to expect ..... most of the Poly buildings are 3 story and only have a balcony on the top floor. The 2nd floor has a slider that opens, but a rail keeps you from going out (and there's no where to go, anyway). There's also the ground floor, which many people with young children like because the kids can play on the grass and you can sit on the patio and watch them while someone is napping inside the room. There may be slightly different balcony set-up in a few of the buildings. At one time, the 3rd floor rooms were the smoking rooms, but I'd be surprised that every building has it blocked off entirely for smokers now.
Over the 20+ years that we've been going to Disney, the trees at the MK have grown, as well as the trees on the islands in the lake and at the Poly. I think this has diminished the view of the MK and the castle, compared to what it used to be. But it's still there

and there's still a view. Like any resort, you could have a tree right outside your room.
The Poly is wonderful, and the rooms are some of the largest, which will be helpful for your large group. It's so convenient to get to the MK via monorail or boat, and if your room is near the TTC, you can walk to the monorail to Epcot. I think that just riding on the monorail and the boats is an adventure itself. We love the little water sprites that you can rent ----- or rent a canopy boat for your entire party and have a relaxing time out on the lake (be sure to go "behind" the Contemporary and see WL and FW).
As others have said, when you book and the type of discount don't seem to have much to do with the room you get. Some of it is when you arrive and if you're willing to wait for a room that might not be ready. Some of it seems to be pixie dust. There's always the option of asking to move, if your room doesn't meet your needs. Hope you have a great trip!