You need a prep sink. With this plan, your sink will be a real haul from your fridge, and the island is a huge barrier smack in the middle of that route. The fridge to sink relationship really doesn't work in this plan. If you want your sink in that location (which comes with the challenge of having an angled dishwasher that can be a trap for person working at the sink, but that can be workable even if undesirable), then without a prep sink I think you have to find a way to get the fridge over into the L, more where the range is in the plan, and then the range would need to be relocated, probably in the wall parallel to the sink, to the left of the sink. I understand your desire for the larger kitchen, but if you go with this plan I think you will find that you have a larger, yet less functional kitchen. What is likely an easier fix than moving the fridge or range placement is adding a prep sink to the left side of the island. Make sure it's a large enough sink to truly be functional. Then the sink on the perimeter can serve as a clean up sink, and you can fully separate your prep and clean up zone. Good luck as you work through it.

Agree with Muriel. You need a prep sink. I'm having a hard time reading your plan but I would make sure you have at least 48" aisles between the island and range. If you want to consolidate your kitchen, you can also do as Muriel suggested and move your range and fridge, but I would still have a prep sink in that layout. It would also require you to change the island layout so no one is sitting on that side, which you may not have space to do.