Well first of all you need to get some proper shoes to ride in!
You have to have a heel! If I came with flat shoes even to a dressage lesson, I would not be allowed to ride. She (my trainer) simply wont train with me. Its very dangerous! Just as important as a helmet. :)
In the "after-pics" you are throwing yourself forward..! You actually don't have to do much (in a maner of speaking). Just sit back and wait for the jump to come. Have contact with the horse so when the jump comes the horses forpart is free of weight and it puts its weight on its back legs. Then as it lifts its forpart to jump, you simply follow and just kinda stand a bit in your stirrups! You practically don't have to move too much, just follow the horse forward (follow, not throw xD Kinda hard to explain for me..). You put your weight in the stirrups and balance. As you are over the jump, put your hands down
so the rein loosens. Don't throw them forward to its neck, as some people do, just put them down on its neck and the release will be there :) So no need to ride with loose reins.
Balance work should be done in dressage work, not in jumping. You should practice standing in your stirrups in walk trot and gallop. Not having contact over jumps isnt very serious, because then your horse is probably not collected (you know, so it can do the whole putting weight in its back legs so it can push off thing)
I'm just giving you a picture of how it should look like.
Its very hard for me to judge on the pictures. I know its mostly your position you are thinking of, but I personally think it almost comes naturally. Half of it is riding the horse right to the jump. Then you will feel it if you're doing something wrong. Either you get left behind or you lean too much forward, and so on. You WILL feel something's wrong and uncomfortable and then its easier to figure out what it is exactly :)
But I think your lower legs do look better, remember bend your knees and don't press your knees to the saddle. You should be able to flap your knees xD
The before pictures doesnt look that bad either just looks like you kinda got left behind a bit.. I dunno.. Just the new pics look better, lets just say that xD
I'd love to see some videos!
It looks like a very sweet horse!