Downlighting at the ceiling level is a pretty crummy way to light up a workspace like a kitchen, since it adds glare & shadows to the work spaces. For counters under wall mounted cabinets, under-cabinet task lighting mounted under the front edge of the cabinet, directed both downward and against the wall has far greater efficacy than anything you can mount at the ceiling. That puts the down-light from the under cabinet fixtures closer to the work, and the cast-back light from the wall fills in the hand shadows.
If there is space between the tops of the cabinets and the ceiling, up-lighting on the front edge of the cabinet tops using the ceiling as a diffuser can deliver high ambient light levels to the room without adding glare or shadows, and can counteract the glare factor of any ceiling mounted downlighting.
You may need to use some down lighting centered on the island to make that a useful work space, which is fine, as long as there is sufficient ambient lighting from other sources to fill in the shadowing and cut the glare. Some kitchen ceiling down lighting could be improved (=higher efficacy at any light level) with cove or valence lighting mounted on other walls for no-glare ambient fill.
There is quite a bit of discussion of these issues online a the Rensselaer Polytechnic Institute's
Lighting Research Center, if you're willing to surf the site a bit. I spent quite a bit of time on that site when making lighting decisions on a major kitchen renovation at my house about 8-9 years ago. Of course they've changed it up considerably since then, but you can start at their
kitchen lighting page.
