Ever read "El joy de rearrangele furnitere"?
That, along with 2 pints of baby oil, and a roll of plastic wrap will either break your wife of moving furniture, break you, or cause you to want to move a little furniture every night. You know you've mastered the art of furniture moving when you wake up the next morning, and your king size bed is on the opposite side of the room from the night before. The author you may ask? Watte doctere de Amoure
Without trying to site a bunch of Code articles, let me throw my 2 cents in. A few years back we did a ton of work for several department stores. All of the display cases were wired from underneath with (as sparky suggested) SO cord, floor receptacles, and twist lock cord caps. If I remember correctly those type of display cases are addressed specifically in the code (the article escapes me at present, George may be on to it).
Now, I wouldn't install a floor plug in a kitchen due to the possibility spilling water into it. If there is enough clearance between the bottom of the island and the floor you could install a "tombstone" type floor plug, and not run the risk of spilled water. Or install a receptacle down low on the wall, cord & plug connect with SO. I think that there is enough "room" in the code to install it so that they get what they want, and you are in compliance with the code. If I find the article later, I will post.