Keep the distance the same each session and work on shortening the time it takes to finish week to week. That's one great way to bump up the fat loss aspect as well as the general conditioning.
I thought your focus was "to loose bodyfat, become fitter, stronger, healthier." If your focus is to pass the military fitness test's run and bodyweight work, your program will be different. 5/3/1 probably wouldn't be the best program choice in that case because the bodyweight stuff would become the priority (and, by definition, would no longer be "assistance"), especially if you can't do that many good reps of each right now.
Again, it's your call. But you need to be 100% clear on your specific before you start.