Man, I wish I had a hill. I live at a beach and am only about a foot above sea level.
Anyway, to answer your question, the sled and the car are not good tools for developing pure speed. I'm sure this is going to piss a lot of people off but let me explain:
When you add resistance to a sprint, you change movement patterns in order to compensate for the extra weight. Basically, it is impossible to push a car or pull a sled with sport-like running mechanics. This is why sleds like the prowler are awesome, while pushing it you are forced into a good sprint position (lots of forward lean, knees driving OUT not UP, feet close to the ground, and short ground contact time). Even with the prowler though, the start of the sprint is all fucked up. The start is really all that matter's in football. With all that said, the sled and the car are excellent conditioning tools that should be used as often as you can tolerate. Higher gpp=faster recovery between plays=being able to move as explosively as possible more often.
The hill is more ideal but still, the start is slow/different than a true sprint/firing out of your stance.
So, how in the hell do you get faster? Speed is a combination of things. Within getting into the physics of it, here is what will make you faster:
Increasing absolute strength (lifting will do this)
Improving running mechanics (check out the POSE method or Defrancos stuff)
Improving reactive strength (very short sprint, box jumps, reactive jumps, dynamic efforts, bounding)
You sound very busy so it will be tough to fit it all in. Keep in mind you are a football player, not a powerlifter. So train accordingly.
Here is what I would suggest you do with your workouts from now on:
This will be the order of skills you work on everytime you go in to train:
1. Dyanmic Warm-up for a long time- Foam roll, lax ball, stretch, dynamic stretch, BW movements... you should be sweating your ass off when you get done with this
2. Pure speed work- Pick a short distance - 10, 20, 30 yards max- do 10 reps with complete rest between each sprint (this is not conditioing). Always come out of a stance and work on a different skill every time (pulling, trapping, reaching, whatever). Keep warming up if you need to but every rep should be MAX SPEED. Rest however long it takes to go as fast as possible. Do these twice a week.
2. Box Jumps/Plyos- I would suggest depth jumps of varying heights, kneeling jumps with weight, or seated box jumps. Again only 10 reps and they all need to be very very fast. This shouldnt make you tired. Do these the other 2 days a week.
3. Lift- Your Normal Lifting
4. Sled, Hill, Car, Whatever- It doesnt matter what you do for conditioning just do it everyday and at least 2 days a week, make it suck really really bad.
5. Light jog for 10mins- this will flush the system and speed recovery
6. Mobility... not stretching- Look up how to do PNF stretching and mobility work with bands. Do this for about 10-15mins. If you run out of time, just do it before you go to bed or right when you wake up. I dont care what anybody says, if you want to be strong, fast, whatever, you need to stretch a whole lot.
This might seem like a lot because it is. I am not of fan of working on so many skills in one session but, like you said, you are busy. If you do follow some sort of plan like this, you may need to back off on assistance work with your lifts and just stick to main lifts plus 1 or 2 exercises to work on weakpoints/prehab.
You dont actually have to do this, just my 2 cents on your situation. haha.