Got it. I would do Q&D Swings+PU 3 days/week, and then 2 days/week of "Easy Strength" lifts/grinds. I wouldn't do more power training with KB ballistics since you don't want to compromise your power for Q&D.
So presses, getups, squats, rows, etc. could work well with 10-15 total reps per exercise, maybe 2-3 exercises per session, and lots of rest in between sets. Basically: don't wear yourself down, exit the workout feeling as fresh as when you started. Alternatively as you suggested, a light jog or ruck but with a moderately low HR (don't push it).