Your cabinetry looks very nice, I can see why you aren't considering replacing it.

In which direction are you considering moving the island (assuming you can do this)?

I would not move it any closer to the range since that aisle is also an aisle used to enter/exit the kitchen to the outside.

As to the prep sink, I prefer it closer to the range. It's close at-hand for draining pasta, for adding water, and for prepping directly from the island to the range. Depending on how you cook, most things go from the refrigerator/pantry to prep to range/MW. I would think unloading the refrigerator onto the island and then going around to prep is preferable to prepping on the refrigerator side and then walking around the island to get to the range.

However, the fact that the range is in a thoroughfare may be reason to pause and think more about it since you will be prepping in that thoroughfare. If it were me, I would probably still leave the sink on the range side...less distance to travel in that thoroughfare w/a pot of hot water.

The real problem in the kitchen is the fact that the refrigerator and range are directly opposite each other with a large island b/w them. If there is any way to address this issue, I think it would make a bigger difference in your kitchen than moving the island and/or prep sink.

Thank you for your comments. I was going to shift the island toward the eating area so that I could almost cross directly from from the fridge to the stove. I agree with your reasons to put the prep sink by the stove but I'm wondering about the times when you are preping a cold meal - then all the cutting boards/knives etc will all be on the other side of the island.