Hi, beautiful kitchen you have! I think a long runner would work and look great.

I have a similar style kitchen and we did a long runner in an indoor/outdoor style. This is the one we used:

http://www.wayfair.com/Safavieh-Courtyard-Brown-Bone-Outdoor-Area-Rug-CY6915-232-FV34736.html

(in the 2'4x12' size)

I have wood floors in my kitchen like you and I got worried about water splashing from the sink and then sitting on the floor. Plus it just looked naked. The indoor/outdoor style means I don't have to worry about staining it or getting it wet. I used this rug tape stuff that is like rug pad material that sticks to the back and it works like a charm. I have no movement whatsoever. It is getting a bit of fraying on the edges from me vacuuming, but I'm not worried. It's cheap enough that I'll just replace every year or two. The brown/beige color doesn't seem to show any dirt or stains.

Are you putting the runner on the side of the island where the cook stands or on the side of the island where the chairs are? If the chairs, you need to make sure that the runner either sits under the chairs or leaves the chair enough space to be able to pull them out without flipping over when they catch the edge of the runner.