Creating a comfortable room
Looking at the sketch of your room, it is unusually interesting from an architectural standpoint. However, with all the windows close to the floor, the long, narrow shape of the room, the two large entries into the space, and the orientation of the fireplace, it’s no wonder you have had problems placing the furniture.
It is obvious that the focal point of the seating area is the fireplace. With this in mind, I think your best bet would be to extend out from the fireplace surround and create a custom-built unit to house the TV, other electronic equipment and serving bar.
If you make this low, only 30 inches high, it would not block your vision or the light from the windows. It would make sense aesthetically because it breaks up the long, narrow room. Functionally, it’s an ideal spot because the TV and fireplace are close to each other as you desired. I would put two armless modular units together against the long wall with two one-arm units angled to each side. The angle of the chairs follows the architectural lines in the room. Between them, as shown, I would place two triangular tables which would be the height of the cushions on the chairs.
This whole grouping would flow together as one because the arms are only to the outside of the angled chairs. In front of the chairs would be the two ottomans, placed at the same angles.
Diagonally across the room, on the wall between the two entries, I would again put two modular units with a triangular table to the left facing. The three triangular tables may be made out of wood or a laminate, depending upon your preference.
Also, keep in mind that arms may be added or removed from any of the modular units, as you desire. There’s plenty of room to do so with this layout and I think the flexibility is important.
This furniture arrangement seats six comfortably and the two ottomans can easily be moved to the side and used for additional seating if necessary.
I would position the grand piano in the far corner and place the dining table parallel to the window wall. This will enable you to have a view through all of the windows while eating.
The serving bar, with enclosed storage below, fills the empty corner and, again, follows the architectural lines of the room.