Beautiful ceiling! Have you considered suspended cable lighting? There are a ton of options with this. You can run them parallel to the beams or follow the slope of the ceiling. There are small disc lights and even drop pendants for cable lights. You can do downlights or a mix of down lighting and uplighting. Some examples: [https://www.houzz.com/photos/flintridge-house-contemporary-kitchen-austin-phvw-vp~24705[(https://www.houzz.com/photos/flintridge-house-contemporary-kitchen-austin-phvw-vp~24705) [https://www.houzz.com/photos/living-rooms-rustic-living-room-cleveland-phvw-vp~8622797[(https://www.houzz.com/photos/living-rooms-rustic-living-room-cleveland-phvw-vp~8622797) [https://www.houzz.com/photos/kitchen-contemporary-kitchen-boston-phvw-vp~958159[(https://www.houzz.com/photos/kitchen-contemporary-kitchen-boston-phvw-vp~958159) If you just search "cable lighting" under the Photos section of Houzz you can see some of the versatile options.

I would have a carpenter box them in and stain them the same color as your floors. I don't mind the extension pieces as long as you treat them the same as the beams. Something like this might be nice: Alternatively, you could ask the architect to design a more decorative truss to put between the extension posts:

Good advice! I may just paint and see how I like it left wood. My only issue with that is I will have to tape it so it doesn’t get ceiling paint on it, and I don’t like tall ladders!! Haha. I’m not sure about the doors. I do like the look, just not sure how I would like it in my home. I’m going to look at more pictures and think about it though.

Guessing the problem is more electrical than structural. With some finished wood panels, or even some pipe fittings (all the rage) and some brackets - you could build a false soffit to house the electrical and mount any type fixture underneath. Did a little section sketch for you, but would probably need to see more to come up with the best solution. Good luck & have fun. -f