Watch a video of single leg power exercises on Outside Television.
There are a few exercises that can aid your preparation for long downhill hikes or runs. You are correct in saying that it's the eccentric muscle contractions that are causing the pain and fatigue. When a muscle shortens as it contracts (like your quads do as you extend your leg), it's called a concentric contraction. When the muscle lengthens as it contracts, as with your quads when you're going downhill, that's an eccentric contraction. Both are part of normal, everyday walking, but walking downhill for a long time puts additional stress on the eccentric contractions because more power is required to counteract the gravity that's accelerating your bodyweight downhill. To make your next downhill hike a bit easier (you'll still be sore, but hopefully not incapacitated), try these exercises:
Squat: This is just your standard squat: feet shoulder-width apart, weight centered through your heels, chest high, gaze forward, with or without added weight-but it's the timing that can make it helpful to you. As you lower your hips toward the floor, don't just drop from a standing position to the point where your thigh is parallel to the ground. Slow it down and pause for a three-second count at the bottom before powering back to a standing position. Do three sets of eight. If you're doing these with weight, go about 10 percent lighter than you normally do so you can complete sets of 8 reps.
Walking Lunges: Start with your feet shoulder-width apart and a dumbbell in each hand. Take a big step forward and let your hips drop until your forward thigh is parallel to the ground. Don't let your forward knee travel past your toes. Drive with your forward leg to rise forward into a standing position and immediately take a big step forward with the opposite leg. Repeat for eight steps with each leg.