In my case it is completely the other way around, my push shot came natural. I just recently (after 18 months) manage to understand the motion for the push shot. First I observed my push shot and I tried to translate the same motion to the push shot, and it was very difficult, I always ended spraying the shot wide. I had to completely change my grip, after that I had to make some minor adjustments for my push shot to work again. But I now have a consistent euro/front pin shot to either side and a very strong long push shot that I can shot long, middle, near and diagonally. I tried and tried until I gave up to do the same thing from pull position.
I just cant seem to shot a long pull, I cannot translate the lateral motion to the ball. It is always to slow.
By the way mi OCD would let me have a different pull shot from my push. I notice that almost everyone makes a pull shot without the recoil motion. Even watching this tutorial didn't help xD
http://www.youtube.com/watch?v=8T28Mie2Zb0I just had to have a pull shot with a recoil motion as with my push. xD
As for the advice: you need to have a relax grip on the handle, only when you are actually tossing the ball is the hand tense. Usually to be able to have a quick lateral motion you need to lift the rod a bit, that way the rod will bend in a slight "U" shape that will translate all you strength and motion to the ball and you will be able to have a quicker toss.
I hope my advise can be of help.
Good luck!