If I try to "never stop pulling" and not pause at least briefly I end up rushing it and I start getting right and left.
What you may not understand is that there can be pulling without movement of the arrow. What Rod Jenkins calls "balanced pulling" is the pulling that occurs during your pause. You can pause as long as you like, in fact, and continue pulling in order to avoid collapse and creeping forward of the arrow.
This is a skill that needs to be learned. During my recent class with Rod, he noticed a slight creep when I reached anchor. Nobody else could see it, but when he videoed me and played it back in slow motion, you could see that when I reached anchor, I relaxed very slightly, the arrow would creep forward infinitesimally, and then I would regain back tension. I was unaware of it, but when I corrected it, my shooting improved.
After the pause, you consciously begin to increase back tension to conclusion. The pause is important to stabilize the arrow, and adjust your sight picture, whether instinctive or gap. When you increase back tension to conclusion, your arrow may begin to move backwards again, but not very much, as your drawing elbow is moving in a "J" shape around toward your backbone, and not directly backwards.
For most of us, the release will happen naturally, without conscious effort to relax the string hand, during this increased back tension to conclusion phase. I know it doesn't happen naturally for some people, and I'm not sure what to advise you if you fall in that category. But I am sure that you should be able to pause while continuing to "never stop pulling."