I think the idea that reducing ground contact time makes you run faster is putting the cart before the horse. Ground contact time, for a specific individual, is controlled by how fast he/she is moving over the ground. Unless the sprinter’s mechanics are altered, the foot strikes the ground in the same relative position (under the body) and leaves the ground at toe off in approximatel the same position as before. In other words, an elite sprinter who improves his max speed doesn’t contact the ground farther behind his center of gravity, and doesn’t toe off earlier in his stride. The ground contact time is shorter simply because he is going faster over the ground, the legs are traveling through space faster, and the foot spends less time on the ground.
The first assumption is the correct one, IMHO, that to go faster you need to apply more force during the alloted ground contact time. To go faster, even more force has to be applied during what is now a shorter contact time.
Improving your ability to generate force, and steepening your personal force/time curve (be able to generate more force and apply it at a higher rate) is what makes you run faster. The ground contact time, while it limits the time alloted to generate force, is an artifact and product of speed, not the other way around, IMHO.