I think you’re hitting rather close to the mark here. Ulitimately, you’ll need to find out what it is your potential UX partners will ultimately gain from the process. This speaks to the concept of UX Evangelism that you’ll often here thrown around haphazardly.
Greg Nudelman explains the concept of UX Evangelism rather well when he says that
…the good news is that the entire situation is completely in your hands. You, the UX professional, hold all the cards and have all the power. If you can prove to the business people, on their terms, that usability improvements will help them meet their monetary goals, those improvements will get implemented every single time. Organizational challenges are there simply so you can prove how much you want to implement improvements."
Most levels of the military aren’t concerned with monetary and budgetary goals, so the goals you’ll likely need to speak to are operational. You’ll need to spend some time thinking about specific UX projects, and how to explain to your different potential users (likely broken down by rank and system interaction) the value proposition of the specific project, and why their participation is important.
I’d also spend some time just listening carefully for people complaining about bad UX, and take note. When it comes time to convince those same people about the value of good UX, you’ll have some additional ammunition at your disposal. While I wouldn’t use other people’s words against them, you can use them as a reminder of why your work is important or to draw paralells between other UX problems and your current project.