I too have this problem and it seems that if I hold my finger down then selecting an item to move is easier. For a short fix, make your island zoomed out, tap the item you want to move, and try to move it away from the map, that tends to work for me. So, if you're zoomed out and the majority of the map is up, move an item towards that direction to unlock it. Does anyone else have a better idea/tip?
