Yay, I'm CLOSE to figuring it out! What I've done works, but there are fat sloppy stitches at the joined edges that I'd like to clean up. Maybe you can figure out how. Here's what I did.
Terminology: I refer to Edge A and Edge B. Those are the ends of the first piece, the one I want to graft into a tube shape. Edge A is always the one on the right, Edge B is always the one on the left. "Slip" means to put the stitch on the right needle, usually preparatory to passing it over. "Pick up" means to put the stitch on the left needle, preparatory to working it. I'm working 10-stitch rows.
First, use waste yarn to secure all stitches of Edge A and Edge B. Remove needles. (photo 1)
Row 1 - CO1, slip first reserved stitch on Edge A, CO6, slip first reserved stitch on Edge B, CO1 (photo 2)
Row 2 - Slip next reserved stitch on Edge A, P1, PSSO, P8, slip1, pick up first reserved stitch on Edge B and purl it, PSSO
Row 3 - Slip next reserved stitch on Edge A, K1, PSSO, K8, slip1, pick up first reserved stitch on Edge B and knit it, PSSO
Repeat Rows 2 and 3 as needed. Once that pattern was established, I started working cables into those 6 st in the center (photo 4 - I didn't post photo 3)
The remaining problem -- other than my counting rows wrong for the cabling -- is those sloppy stitches at the joins. Any ideas?