I agree with the Cooks Kitchen. We had a very similar problem. We had a paneled vaulted ceiling, painted white, in a bedroom. There was no insulation in the ceiling...just the wood paneling, then roof paper and then composite shingles. We never had a leak but we would get mold/mildew (it was grey in color) on the ceiling. This room was on the shady side (not sure if that made a difference) of our one story house, not near any bathrooms or laundry. This mold/mildew would build up over time. Every year I would wipe the ceiling with bleach (we had wood-looking linoleum so I didn’t have to worry about bleaching carpet ) . We finally put in a heater with the vents high up in the wall. This ventilation helped a bit but still had to bleach the ceiling every couple years. We are in the process of remodeling this side of the house. Hopefully the insulation will make the difference. In the meantime maybe try a dehumidifier or heater or some fans. Good luck.

Leave the walls/beams as is. Paint everything that is neither, white. For instance, the closets/louvred doors in kitchen, paint white. The raiing/risers on the stairs, and the island paint white, as well. As for a white, White Dove can go very gray without good natural light. With all that natural color wood in the house, I’d use B.M. Simply white for the simple reason it is warmer. Do a gloss finish on cabs and replace counter with a whitish quartz or even the new Wilsonart laminates.

If your room can take a 13' 2” or 15’ width, off the bolt, this is my suggestion. So, on measurementfor the room can’t be wider that either choices. This carpet cannot be seamed. What it means to you is tremendous savings because there is little or no waste. Many choices is the Anywhere collection and all will work with your walls. This is tough stuff with a $$$$$$$$ look. Love it. Next house, I would be it all through the house. https://www.stantoncarpet.com/gallerylist/ANYWHERE%20COLLECTION

"featuring a beveled edge cut on the top and bottom of each plank so they overlap and form a watertight seal." Really? Where is that on shiplap? How often do you see true rough sawn lumber siding used for interior shiplap? Most interior shiplap is not true ship lap but made to look like ship lap. And why would a watertight seal be needed for an interior wall?