Move heat out of living room with fireplace
We had the same situation in my son's home in upstate New York. He had a wood-burning stove and needed to distribute the heat more evenly throughout the house. We installed room-to-room quiet low-speed circulating fans high in the walls between rooms. They could possibly be installed in your louvered transoms or next to them.
His home was all one level which yours is not so you may need a more beefed-up circulating system to reach other levels.
However, I noticed in your pictures that you have a stairwell outside the living room area. An efficient room-to-room fan in the living room wall could move heat to the stairwell that would then rise by convection to the second level. It might be at least a partial solution for you. Below is one Panasonic in-wall fan I found that might work for you - but there are others out there.