I am curious as to what your instructor was doing when you encountered your strong uke, and how much actual instruction you receive on how to attack.
I regularly instruct in Holland, where some of the younger men are very tall and very strong. I can tell you it is quite a change from what I am used to here in Japan, and a welcome change, I might add. At my last seminar the technical level ranged from 5th dan to complete beginners and we spent an entire day on ushiro waza. As usual, there was a wide spectrum of attitudes, from the 2nd dan who felt that aikido should be practised 'softly', to a couple of 1st kyu and shodans, for whom the technique had to work, no matter what.
It is not my practice to use one particular uke unless there is a special reason for it, so for me there is one solution for beginners who think that the techniques do not work: use them as uke and show that they really do work.
I agree with Chris Li that the overall responsibility for making the technique work lies with tori / nage. That said, you should expect to find a difference in being atacked by a strong beginner and a 4th dan, for example (and the 4th dan should be harder to throw). I also agree with Robert Cronin that the senior students set the tone for the dojo, so to speak, and you might look at how they deal with your strong 6th kyu. But I also have separate classes for yudansha and instructors, and have come to believe in the importance of this. I wonder if this is common practice.
Oh, and I do not believe in moving before the second hand has been grasped in ushiro ryote-dori. Of course you might well do this, but the technique should also work from a static position, with both hands grasped strongly. If it does not, there is something wrong.