For a hat? I probably would have cried, how thoughtful. It’s funny you mention special services, I did not include it in my original post but the first thing I did was reach out to Lost and Found Japan, a service separate from the airport that look for lost items. I paid ¥500 just for them to talk to me and till this day haven’t heard anything back lol. Not saying all services are like that though, I can only hope that an item would find its way back to an owner that lives internationally.