Wonderful decor! You could add a warm sky color in the ceiling, a lighter, not darker version of the wall color, or just the wall color. See Houzz photos under "tray ceiling" for examples of how each of these change the look. Some bring the ceiling down, others seem to make it higher. Another interesting and elegant possibility would be metal leaf. Painstaking but dramatic.

I would paint the ceiling the same color. It will look darker because of the coffered. See how the edge looks darker .. the same will happen to the ceiling. test a corner and you will see

Is there a reason you don't like a white ceiling? It offers a crisp contrast to the walls and makes it look fresh and clean. If you really want a colour I would do a lighter version of the rocky road on the ceiling.

to me the white celling has an unfinished look. Like you haven't decided what to do yet. Im also a crown moulding nut. The more you paint around the crown the more just pops out.

I ALWAYS paint ceilings a color and I have also wallpapered them..often with a gold or silver leaf paper. Some metallic papers now have geometric patterns and look great on a ceiling. As I do not see much pattern in this room, that is what I would suggest. Here is just a small example from Phillip Jefferies..

https://www.phillipjeffries.com/product-finder.php?s=detailed&subtype_42=1&pp=72

I second the metallic idea. It would be an undertaking, but leafing the ceiling with a burnished copper would really finish this room. If leafing is too much, exploring metallic paint options, like the Brushed Metallic line from Sherwin Williams, could be a great alternative (SW Brushed Metallic). It takes some technique, but isn't that difficult once you get the hang of it.

Beautiful decor by the way. Whatever you decide for the ceiling is sure to compliment an already outstanding room.