I stopped once to move a big snapper but he wasn't having it. A guy in a truck stopped around the same time and approached with a snow shovel with this sort of weary confidence, like he'd done this a thousand times.

He tapped it gently on the shell, then put the shovel in front of its face. The turtle chomped right on and he pulled it off the road. I don't know if that was the right way to move it but it worked - mostly I was impressed he had a turtle-moving protocol (and shovel) ready to go.