I must be doing something right.

Because I found this diagram on some kitchen design site displaying pretty much exactly what I intend to do. Except that my refrigerator will proportionally be about three times the one rendered here. Anyway, it properly represents the classic "kitchen work triangle" concept (not to be confused with the "upside-down pink triangle", which will likely never see the inside of my kitchen). 

Gonna skew the sink to the left (it'd be to the right in this pic, but it's technically upside down), then have the dishwaster beneath, to the right side of the island. Currently trying to figure out which Ikea cabinets you combine to achieve this. Their "built-in" islands are really just combinations of cabs, and none of them are wider than 24". Pretty sure my sink will be wider than that (the current ugly one by the wall is around 31"), so I think I may be flying by the seat of my pants here.