I have found a practical answer, but would be interested in comments filling in detail from anyone who knows how this works.
The problem did prove to be to do with how the CALayer was being stretched. I was drawing into a bitmap of arbitrary size, on the basis that (as the CALayer docs suggest) use of a .contentsCenter with zero width and height would in effect do a nine-part-image stretch, selecting the single centre pixel as the central stretching portion. With this bitmap as a layer's .contents, I could then resize the CALayer to any desired size (down or up).
Turns out that the 'artibrary size' was the problem. Something odd happens in the way CALayer stretches the edge portions (at least when resizing down). By instead making the initial frame for drawing tiny (ie. just big enough to fit my outline drawing plus a couple of pixels for the central stretching portion), nothing spurious makes its way into the edges during stretching.
The bitmap stretches properly if created with rect just big enough to fit the contents and stretchable center pixel, ie.:
NSRect rect = NSMakeRect(0, 0, lineWidth * 2 + 2, lineWidth * 2 + 2);
This tiny image stretches to any larger size perfectly.