So you're right in thinking that adults are maybe overthinking things.
Andrew, you are a class act!
Yes! Exactly my point, over-thinking something that comes natural since most of us have been pedaling one thing or another since just after learning to walk. I don't recall ever having anyone ask "how can I more efficiently walk up a hill?" Though it could be argued that the hiking community might discuss such things.
But, since the OP is (probably) an adult and wants to tidy up his form, he can certainly do it faster by doing some drills...
Yes practice. Even mimi says it
... there's no magic solution for better pedaling stroke just lots of hard work and practice...
to do anything else would be
Unfortunately you didn't read the op again. He does what feels natural to him but it does not work that's why he's here asking for help. You then suggested that he asks a 3 year old. Good for you hundun.
OK, for you, mimi, I reread the OP.
Such a simple subject is easily approached with zen mind(as uncluttered and unbiased as the mind of a child).
I know with clipless pedals your supposed to use a circular push pull motion. Does this apply to flats as well? If so is the pulling motion accomplished by pulling up on the pedal with traction from the pegs and shoes
Obviously, it's a combination of two things which brings the pedal up with flats, the down-force of the opposite pedal and momentum. So the answer is no - it does not apply to flats as well.
...I am killing myself on climbs with my horrible technique of just putting my weight into the pedals...
Since the issue of practice has already been addressed, let's discuss some obvious issues regarding a hill. Speed and momentum on approach is your friend. Then we are faced with a choice: Do I use a lower gear and spin pedals really fast, or do I use a slightly higher gear and use slower power strokes? Take a hill and try it between the two choices to get a feel for when one choice best trumps the other. Deciding factors will depend on gradient, distance, momentum, strength, and so on.
A zen mind will calculate, decide, and adjust without even thinking about it.
Enjoy the ride. Don't over analyze it.