1. Stop Distance running
A 60 Yard dash is a relatively short sprint. There is very little aerobic component to a sprint at this distance. Be very careful not to let your speed training sessions turn into conditioning. You should always allow for adequate rest times.
It should go without saying that distance running will not help you improve your 60 time. Distance runners tend have short hip flexors, weak glutes, and overall poor hip mobility.
2. Develop a Drive Phase
The drive phase is the acceleration portion of a sprint. It's taught all the time in track, but for some reason it gets lost on baseball players.
An experienced sprinter can drive for up to 40 to 50 yards. The goal should be to accelerate as long as possible and slowly rise up like an airplane at takeoff. The longer you can accelerate the faster your top speed will be.
During the drive phase the eyes should be down, the shin angle ideally around 45 degrees, and the foot should strike the ground directly underneath, or slightly behind the hips. The goal is to be powerful, and get triple extension from the ankle, knee, and hip.
Sled pushes and drags are a great tool for acceleration development because it will put you in the proper acceleration mechanics with hardly any cueing. The sled forces you to run at the proper angle and to drive into the ground.
3. Get Stronger
This is what the glutes and hamstrings look like on an elite level sprinter. If you're not spending a considerable amount of time in the weight room you're doing it wrong.
4. Stop Worrying About Quick Feet
Speed equals distance over time. Quick feet are essentially useless if you don't go anywhere. Focusing on getting a powerful drive from the hips is going to increase stride length and is far more beneficial.
Our ground contact time should be longest at the start and slowly decrease as we accelerate. Quick feet without any force application is just spinning your wheels, and you're not going anywhere.
As you slowly start to come up out of your drive phase let yourself relax. It should almost feel as if you're floating.... A relaxed muscle is a fast muscle.
One of the biggest mistakes I see is athlete's muscling up to try and run faster. This is wasted energy. The face, neck, and shoulders should all be relaxed.
Fast people make it look easy.