Its when I'm asked to pause at the control stage (point where I'm about to throw) that I have problems. I think I tend to lose it there. And now that you mention it, as Uke finds his feet they tend to receive more pain.
If you pause at the point just before the throw and uke is finding his feet, then perhaps you haven't quite got his balance?
Last Friday class my Sensei was demonstrating this with our 2nd kyu student as uke, and had him leaning backwards, mostly off-balance, with uke's arm under Sensei's control. The final part of the throw was a sword cut movement of tori's wrists which takes uke completely off balance. Uke wasn't in great pain but he wasn't comfortable either, and Sensei was in a good position to control him if he decided to try to regain his balance...