The OP says that to attacker's actually changing up the direction and intent of the attack to turn it into a yonkyo if he doesn't react in time to the incoming energy. That's a lot of incoming energy and I would say that's probably not the problem the instructor is wanting nage to solve.
Trouble is, turning the attack into something like a yonkyo is probably the appropriate thing for the attacker to be doing in this situation. What else would they do? Freeze there and wait for you to sock them with your other hand?
So I'm sympathetic to an uke who's trying to make his attack realistic. The trouble is that you have two people trying to practice above their pay grade--an uke who (so far as we know) doesn't really know if his attack is realistic or not, and the OP who admits he can't handle that attack with his current skills.
And Szczpcz to the contrary, you're not likely to learn anything useful in this situation. The OP is more likely to learn to muscle through the technique than anything else, and the uke isn't learning how his attack has left him open (if it is).
But, given that people are jerks and you mostly have to deal with them as they are, my strategy is to take them as a challenge--how can I deal with them without
muscling up? Has their attack left them open? Can I take advantage of that with a little atemi? How does atemi (gently, bloodstains are a pain to get out of the mat) change the situation? If the attack prevents moving the way I thought, how can I move? How can I unbalance them?
The result may not look a whole lot like the technique we're supposed to practice, but at least it's useful to me, which trying to power through it would not be.