And here is the proof.
After knitting 3 (THREE) joining strips, I flipped the work over only to find that the back of the joining strips looks really nice. I mean REALLY nice. That's when it hit me. I like the back side best, don't you?
The original strip is on the left. The upside-down strip is on the right. No contest, right? (Ignore the faint turquoise line on each side of the joining strip. That's just my lifeline that I'm leaving in place for the moment.)
In my defense, there are a lot of variations possible in this process. If you slip the stitches that need slipping in a purl-wise fashion, the result will be different from what you get if you slip them knit-wise. If you join with a slip one, knit one, pass slipped stitch over manoeuver, it will look different from joining by purling 2 stitches through the back loop (from the back). There's a lot of trial and error and a lot of just doing it the way you like best. There's no absolutely right way to do any of this.
For those who are still wondering about it, this insertion is a little like adding an edging to a knit shawl. There is no grafting involved, nor is there any sewing. I don't have anything against grafting or sewing, but I find this process very intuitive and pleasant and versatile.
Once you figure out which side you're on.