The shawl itself is complicated, so we wanted a simple edging. But all the simple edgings we tried were visually boring. More importantly, they were insubstantial and didn't frame the shawl very well. It occurred to me that part of the problem was that all the edgings we sampled were real lace knitting, that is, patterned on both sides. After perusing a few lace books, we decided that such edgings looked floopy--they were elegant flat on the floor, but when vertical, the edgings seemed droopy instead of crisp, and detracted from the overall appearance.
We reshelved all the lace books and fired up Excel instead. Within an hour of fiddling, we had a simple, but visually dynamic edging that worked well as a frame for the complex center. And the return row was plain knitting, so it would be easy to knit backwards during the attachment process (I hate turning knitting and avoid it whenever possible). Finally, the 16-stitch repeat fits perfectly into the 32-stitch repeat on the border.

Harry remarked that I had incorporated the Soba Noodle motif that he had originally planned for the edging, and was pleased by the smattering of Pachinko balls that I managed to scatter inside the points.
The next step was to actually start the edging. Where? I didn't want to begin at the corner, because I wasn't exactly sure how many doubles (attach two border stitches to one edge stitch) I would need to go around the point. After two hours of research on and off the Web, I realized that not a single person ever revealed exactly where they started their edging attachment. Weird, considering that long, convoluted paragraphs were spent on esoteric arithmetic calculations that made my brain fizz gently.
I decided to begin after the corner stitches, going clockwise around the shawl. This gives me plenty of practice before I get to the corner.
Here's a diagram:

I am planning 8 doubles on each side of a corner using Fleegle's Easy-To-Remember Rule of Corner Turning, which states that the number of doubles needed to go around a corner equals half the number of rows in the repeat. This rule works fairly well for most edgings. I don't like triples--way too bulky and they put a bit of a strain on the poor corner stitch--so I avoid them.
Anyway, you can finally see a bit of the shawl emerging;

Harry is ecstatic--me too!