Having made my somewhat violent suggestions earlier, it might also be worth considering the following.
What is the difference between udekime-nage and kokyu-nage? I would suggest there is very little difference apart from the pressure on the elbow. Please watch the video below to see what I mean.
So, if you are having trouble with the technique, it might be because a) you are focusing too much on the elbow, and b) you aren't getting all the other aspects that make this essentially a kokyu-nage. Are you able to do the technique shown in the video?