My installation went as smoothly as one could hope. I followed the suggestion of one of the Apple Store's geniuses and put my new drive in the enclosure first.
Then I CCC'd what I wanted over to it.
Then I just switched out the drives.
The only problem which arose was that I couldn't use iView MediaPro to show some recently shot Nikon NEF files. Drove me crazy.
Well, it turned out to have nothing to do with the drives, but rather with a update for NikonView software which I had done a day or two earlier.
So my lesson learned was not to attribute problems to the most recent change, but to think about what else I have been doing recently.
Another important point for me was to use the same names for the partitions on my new drive as the ones I had been using before. By doing this I ensured that Applescripts, etc., were not confused.
I've been using the old drive, still in the enclosure, exclusively for music files now, having changed it to a single partition and renaming it.