I like the drop-cord idea; then I stared thinking: what if there were a stove/hood on the island, rather than a sink. Would receptacles on the side of the hood work?
Oops! I almost forgot the 18" rule, and the short cords on kitchen appliances.
Wait a minute- if they make pop-up range hoods, why can't they make pop-up receptacles?
Or, maybe use an office-furniture style
cord pass-through, to a receptacle mounted inside the cabinets?
I'm looking for ideas here....