I would hire an electrician to add cans everywhere, kitchen also. You can't get that kind of light with just a fixture hanging from the ceiling. A fan or a chandelier is nice to anchor the space with, but you need cans with those high ceilings.

This works well for us, cans on the sides and a chandelier centered. Yes, a weird angle for the picture, I tried to capture all of them. A licenced electrician will be able to help you with the correct distance from each other depending on your ceiling height. Good luck!

PS. while the chandelier placement looks awkward from this angle, it hangs in the center of the dining room.