If you ask Tracy E. Thomas, living with cancer becomes much easier when you learn to shift your focus to something else. For him, that’s meant turning to filmmaking.

“It keeps me alive, and it sustains me,” he says.

In fact, this is part of the reason the feature film stuntman refused to turn down opportunities to work on blockbuster movies such as “The Hunger Games: Catching Fire” and “Dawn of the Planet of the Apes” while...