When you say, "I can feel my foot pads sort of shifting and sliding under me", my bet is you're not engaging your toes enough, and of course the balls of your feet are squirming under you. Land on the outside of the balls, and roll to the inside at the same time you engage your toes. Your toes are not just "along for the ride"; they're there to be used. When running uphill, engage the toes and pull with your glutes. Remain upright (posture!) and avoid the tendency to lean forward and push up and off.
When running downhill, arch your toes upward (called dorsiflexion, if I remember correctly), bend your knees, reach down to meet the ground, and then use your toes to grab the ground to prevent sliding forward on the balls of your feet. Keep a short, fast stride, even downhill. Forget about speed going downhill; maintaining technique is more important to protect your feet.