Hi,
Umm my two cent worth are:
Practice on a long steady climb with smooth surface, ride in a slightly larger gear but at a low effort...say 65 cadence but 60%heart rate effort. Concentrate not on pushing down but pulling through the bottom of the stoke with each leg "scape the gum of your sole", you want to grab the pedal as early as you can and pull it through, then once you have mastered that do the same but just try to get into the top of the stroke early "kicking a ball with your toe", work on this and when you ride do efforts of pedaling effieciently. Over a period on months you will retrain your nervous system and the muscles will get stronger, especially the hamstrings which are often underutilised by cyclists. Remember as your increase you downstroke effort increase the effort to pull through too, it will save you quads a heap. Do no pull up with your hip flexors, it is not worth it.
btw takes practice over 1 month at least to get smooth.
Ian