I am new to lifting – caveat – so I refrain from giving technical advice there. However, I was a pretty damn good runner and was known for having a smooth, efficient stride.
One thing I can tell you (aside from any specific imbalances you may need to address) is that long, slow running is much more tolerant of crappy form (at least in the short term) than fast running. You can point your toes out, lurch, shuffle, waddle, stomp, favor one leg, tilt your pelvis funny and still run along at a slow pace provided your aerobic conditioning is any good.
Going fast, however, demands that you be efficient in your movement – the faster you go, the more efficient you need to be.
Try finding a flat, not-too-jarring place (a football field or the rubberized track running around it) and doing some accelerations/decelerations. Start slow, accelerate smoothly up to maybe 90% of your sprint speed, then decelerate smoothly all the way to a stop.
While you do this, you can pay attention to your alignment (and to the usual cues – shoulders down, face relaxed, hands relaxed, gaze ahead not at the ground) – but don’t obsess over it. You might find that much of it is fixed automatically. What you’re shooting for is a feeling of smooth power all the way up and down your speedometer. (Being smooth in acceleration and deceleration isn’t wimpy – it takes strength and develops strength.) Don’t let yourself stomp (people do that when they’re tired and it accentuates weaknesses) or run lazy.
When you “get it” (likely gradually) it should feel like everything – arms, legs, everything – is working together to propel you forward. I used to imagine a big gear at my center, connecting my extremities and off of which everything ran.
Also, 90% isn’t a fixed threshold – go up as fast as you can while staying smooth, then cycle down. If you push this a little every time, you’ll eventually be able to hit top speed and hold it without breaking form. As you get better, you’ll also be able to accelerate and decelerate more quickly.
This strength/smoothness should carry over into your slow runs and help to improve your form (in addition to any other corrective work you may do).