This evening I decided to experiment with a solution and, IT WORKED. So I thought I'd share it here.
I simply allowed the milk/cheese mess to cool from its "hot" condition to a temperature closer to that at which I might have originally added the cheese successfully. I then poured the mess into my blender, started on low speed and then immediately to a medium speed. I allowed the machine to run about a minute, then poured out a beautiful sauce.
It's a tip that some of you may have already recorded in your cookbooks. But I had never heard of it before I got the good results I achieved today so I hope this hint helps someone else who may run up against this problem in the future. :lips: