I spent time each summer on an Island at Winnipesaukee and I loved it. No noise no cars relaxing it was great. Here is what I learned.
You need to haul EVERYTHING by boat to Island home( IH). You must have a slip on the mainland. You are limited to use from Ice in to Ice out. Water from the lake, septic issues, power availability, heat source just a few of things come to mind that are a little different from main land living. We had SW exposure and it was great. I would say if you have the time, rent a place near where you would like to be for a month both mainland and island. Then make your final plan. Good luck!! I wish I had your problem!!!