Hi Beth,
I'm a spinner, too, with tubs of yarn to weave into blankets and (if I get really brave) a tunic. You're ahead of me in the process, because I haven't started weaving the blanket wool yet. I was waiting for the double-weave lessons in Season 3. So please take any of my suggestions with a grain of salt.
First, I don't know how thick/heavy/drapey your wool is. Nine feet is an awful lot to balance on your lap! Can you use a table? Even a folding table could help. When I've machine quilted, I've rolled the quilt at both ends and that's been helpful, but still awfully awkward. Do you have or can you borrow from a friend or the library, the Alabama Stitch Book by Natalie Chanin of Alabama Chanin? I was looking at stitches. The backstitch might be a good idea for sewing it together. I don't think the blanket stitch will hold the panels together over time. It's good for edging though and can be pretty.
I have a treasured handmade blanket by my former mother-in-law. She was a weaver in Tibet. I'll try to upload the picture. It looks like she laid the panels next to each other and did a whip stitch to join them. It isn't fancy, but it's held together for at least 40 years and probably more than that. As I typed it, I realized that the whip stitching she did is like backstitching because the stitch is on the front and back of the fabric. I don't know how to use a serger. Is there some way you can serge them together? If you use a regular sewing machine, a walking foot would be very helpful.
Good luck!
Cynthia
Oops, not sure how to upload a photo.