Galimberti's photos twist the cultural conversation by revealing a disparity in economic privilege across his subjects.
The most precise version for twist in the above sentence is extend.
Galimberti's photos twisting the cultural conversation and revealing a disparity in economic privilege is proof that there was no prior knowledge of the disparity in economic privilege across his subjects. So, his photos extended the cultural conversation and brought the disparity to light.
This makes extend the most precise option for the replacement of twist.
