Today, I figured out that there is a working pw.x executable for Quantum Espresso on the DoD machines Conrad and Gordon. It is located in /app/espresso/6.3-intel/bin. All you need is a PBS script with an execution line like

aprun -n 32 /app/espresso/6.3-intel/bin/pw.x < qe.in > qe.out

Also, you need to do module load intel prior to submitting the job. You can either add a line in your .bashrc or place it in the PBS script. Enjoy!