Good fences make good neighbors

My next-door neighbors recently had eleven trees, all old pines, removed from their yard. Until they started their landscaping project, the back yard fence that runs between my property and theirs was mercifully concealed by a thick growth of azaleas, gardenias, and just plain vines and briars on both sides. Now the fence is exposed and shows its makeshift nature. It's part rotting lattice, part chicken wire, part hardware cloth, and a real eyesore. I realized I would have to replace the fence, called the Renovator Guy I've grown so close to, to have him tell me that I'd need to have the line surveyed. That took some doing. I thought I knew where the line was, but now there's an orange stake showing how wrong I was. I own about ten more feet of land than I thought I did. In fact, I could almost charge rent for the neighbors' mailbox! (In the picture, you can barely make out the stake behind their mailbox---that's my house to the right.) So NOW what do I do? Build the fence along the line? One of the reasons my neighbors took out trees was to allow access to their back yard. Turns out it was MY tree that came down to allow that to happen. But if I build the fence where I THOUGHT the line was, they'll have to maintain part of my land--or I'll have to maintain a strip on their side of the fence. And if I build it on the line, they won't be able to get into their back yard with a truck. Dilemma! And I can't just think about them, because they may not always own the property. Or I may not always own this place. What to do, what to do?