I didn't realize that you already had the strips made. Let's see.. . .
You can really take off a cast-on easily. You could take off the bind off of both and do a three-needle bind off. It leaves a nice-looking seam, but leaves a ridge across the back.
How about edge-to-edge seaming?
Picking up stitches would work if you were going to knit the new piece on, but it's too late for that.