I would use something similar to the item below. Just make sure the lights are placed more towards the island seating area than directly over the stove.

I think I would go with something without such a long drop and while you are at it change that boob light too.

I would change the dome light in the kitchen to more of a hanging style light to give you more light, then for over the stove I would maybe pick something that doesn't hang down so far over your stove, so you have plenty of room to cook and don't constantly have to clean grease off it.

Get an overhead hood with a good LED light and put that antique, doesn't work, active nuisance of a downdraft out of it's misery. You are going to hate it.

I would go with Canned lighting:

http://amzn.to/2f8IgEn

Patricia Colwell Consulting I really dislike all of the boob lights!