I can understand your problem very well because it's just the same at our training.
Training at the sports center of our university is almost free, so there are a lot of people with karate or ju-jutsu background visiting our beginners class.
My observation is that those people focus entirely on hands and feet of their partner and therefore have problems with distance, timing and orientation which make them try to force techniques.
The first step to make those people relax is to let them realise that they are not attacked by hands and feet, but by a whole person and therefore have to deal with their partner. To do that, it's necessary to look in your partners eyes which is very difficult for some people.
Soon after starting to deal with persons instead of hands, most people develop good timing, distance and orientation.
Knowing what's going on and being in control helps very well to relax, to center and to understand what the techniques are about.
A better orientation normaly leads to a big improvement of ukemi, too.
This works very well in our classes and I hope it's of some help.