"And when I try to do anything to make it happen it feels contrived"
If you ever talk to any golfers who have lessons, especially beginners, they will tell you that when the teaching pro changes their grip, or stance, or whatever; it feels "wrong" or "alien" or "very different". For some people that is too much and when they can't hit the ball well they revert to their old habits. For those who can be bothered they quickly become acclimated to the change.
There's a lot of discussion about how long it takes to ingrain a change ... there are figures of 10,000 reps, 20,000 reps, 6-10hours bandied around. I'd imagine that in running terms it would be about 40-50K concentrated effort on the heel flick.
It would worth getting someone to film you running. I'd assume that your comments are only based on kinaesthetic feeling of what is happening with your running as it is obscured from your vision behind you. You might find that you are doing the correct movement already if you look at it on film.
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