Is the island open? I mean, is it just the countertop, and no upper cabinets?
If so, it is close to what I have. I ended up putting the rear surrounds in the kitchen on top of the cupboard, one on each end. Just dial in enough delay to compensate. As for the side surrounds, put the left one in the same place you were going to put the rear (left of door), and the right surround put on same corner as you have in drawing.
Check the floorplan I attached.
I wanted to keep the speakers near the seating area too, but when I am listening to music, wherever I am in either room, I get good sound.