While you're waiting to see if benjesbride's idea is doable (now I'm the one who is confused ;), this is the kitchen with a more squared island. It wouldn't be square, because to have cabinets facing the cooktop, then 2 seats on the bottom side, the island would need to be 6' on that side (each seat needs 24" elbow room.) With 24" cabinets on the top wall, and a 48" aisle, a 58" island leaves only about 37". That's fine for a walkway, but you need more room to walk behind stools. If no traffic will be in that aisle, it would be tight, but it would work. I want to point out the the fridge door and handle will protrude into the 48" aisle, but the NKBA recommended minimum is 42", so I think that would be OK, since there would be no sink on that side.
That leaves the prep space issue. I drew the plan earlier to show you the available prep space on an island turned 90°. Ap. 27" of prep space is a non-starter for me, unless it's in a tiny apartment in a high-cost urban area. There would be no landing space for dishes on one side of the sink, and you'd be prepping over the DW. Making the island square would do nothing to improve the function of that work zone.
In addition, what I tried to illustrate with the crossing yellow lines, is the inefficiency of the work flow. Instead of being able to take items directly from the fridge to the sink, you'd need to walk around the end of the island to get to the sink. A helper could not load or unload the DW while you are prepping, because, as mentioned, you have to prep over the DW. If you needed something from the fridge or pantry, once you started to cook, anyone unloading the DW, or gathering dishes to set the table, would be squarely in your path. You would still have the nice secondary prep space, but it has no water source, and with the location of the DW, that's the logical space for dish storage.
In the changes to the first plan I posted, if you think the fridge is too far toward the cooktop wall, it could be switched with the pantry. The island could still be used as landing space, and there would be a shallow landing space on the dish hutch on the right side. Or, instead of a hutch style cabinet, you could have uppers and drawer bases for dish storage, a counter for landing space, and a coffee/snack center.
The following plan illustrates the problem with the deeper island. The only advantages I see would be a spot for a cool pet bed in the middle, and two seats have a view to the left.
Original orientation of island, with fridge and pantry switched:
Another version with the fridge closer to the DR:
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raw edge
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