If the first stitch is a knit you would want a purl to appear to its right so purl into the front of that first knit stitch, don't take it off the needle, then knit into it. At the end the last stitch is a purl and you want a knit to its left so that last purl stitch, purl it then without taking it off the needle, knit it. I tried knitting several row increasing on the right side that way and it worked, and looked good. I didn't work into the backs of stitches, just knitted and purled the stitches in the normal spots. The rows between the increases just make sure you work the ribbing in sequence.
The next row you need to increase ends up with a purl at the beginning so knit it and then purl it. At the end you have a knit stitch so knit it then purl it.
I also tried doing the second half of each knit front, purl back or purl front, knit back through the back loop and that works too, but I don't know that it is any great improvement.