Lean from the ankles, not the waist
Drive your whole torso forward as one piece, with the lean coming from your ankles and hips, not a hunched lower back. Keep your upper body stacked roughly over your feet so your weight helps push you up the hill instead of hanging out behind you. A collapsed, rounded posture chokes your breathing and kills your push.
Pair that with short, quick, constant steps instead of long lunges. Small steps keep your cadence up, save your hip flexors, and let you keep moving over rough ground. On a steep pitch, a relentless short stride beats the occasional big heave every time.