Like most people have been saying, many trainers have their students go into two point a couple strides early when they are first learning to jump. The proper way is to go into two point as your horse is taking off. This is a very hard concept for people who are somewhat green to jumping because it has a lot to do with feel and distance and finding your spot. That is the reason why trainers like to teach students to start early, so that they will be ready for the jump and in the correct postition. The problem with going into two point early is the issue of refusing. Many horses tend to refuse if they are not ridden all the way up to the jump and if you are already in two point it is much more likely that you will fall over the jump then if you are sitting up.
If you feel unsure about jumping, what I would suggest is to go back to ground poles. Canter over ground poles and feel your horses striding. Do not go into a full out two point, but sit a little more foreward over the pole and make sure to move with your horse. You will soon learn to feel the striding and how your horse takes the jump. Timing and distances are both aspects of jumping that will come over time. Just be patient.
If I were you, I would definitely ditch the western saddle. I known the saddle horn makes you feel more safe, but it is not good for your horses back to jump in this saddle, nor your position. The best thing you can do, if you are worried about the refusing, is to be confident. Look ahead, put your heels down and act as if you are going over that jump no matter what. This will give your horse more confidence. This will help your position because it is rather hard to go into two point with a huge horn poking you the whole time.