For a very long time I was not able to center clay well; just didn't seem to get it. I got it "good enough", but never well centered. Then, I saw a Robin Hopper video on centering and his method and explanation worked wonders for me. Robin pointed out that the spinning clay is coming toward your right hand and if you oppose the spin with the unmoving right hand, the clay has to either push you out of the way, or yield and go up. Up is controlled with the right hand on top. It is basic, good sense, advice, but sometimes changing your approach to a problem is what is needed. It may not help you, but it is worth review to see if it may. You may have developed methods over years of potting that are not working for you with your issues, and a slight adjustment may be just what you need.
Best of luck,