That vault looks very nice. I would recommend to mount the fixture roughly 7' above finish floor. so the bottom of fixture would be at 84" from floor, 48" above counter. This would allow it to project down from the vault enough to be exposed but not too low in the space.

I would need to see the light I see 3 spots with electrical so why are tey there if you are doing one fixture.IMO island lighting should light the island surface so ralerely would I iuse a candelier type lighting . I think I need to know what the reason was for the barrel ceiling it semms kind of lost in the space .

Patricia Colwell Consulting, this is the chandelier. It comes with a 12” and 24” rod, but I can purchase another which will be necessary. I’m unsure of the reasoning behind the barrel ceiling as I didn’t design it. I purchased the house from the original owner. I can only assume it was done simply for aesthetic purposes.

Do you want to actually light the room and the island and have a functional working kitchen? Or is it all for show, and no one cooks? Because the entire lighting plan needs a revamp if you want the whole kitchen lit to work in, without shadows that interfere with you seeing what you are doing.