What about tin or brick at the bottom and then wire from a certain height upwards. You'd be surprised how much they will try to climb, and he falls at a decent height and lands on his back it could prove hazardous. I would be using a non wire product around the bottom, just high enough that they can't reach up. I know you won't want to spoil the look of the enclosure with a non-see through fence but you still need to consider safety for turtle, too.
I do voluntary work at wildlife park with the reptiles and I was surprised just how far a hungry turtle will try to stretch and climb to get the food. He has glass fence around him but has a rock feature at one end where he tries to climb. Its not tall enough for him to hurt himself but he is always falling backwards, working overtime to catch the food out of my hands.