OK, so I lined the scarf according to the TECHknitting blog's instructions. I sewed the lining to the scarf with the overcast stitch, also instructed on the same blog.
I used soft cotton muslin for the lining, and it seems to work out just fine. I wasn't sure if it would be sturdy enough to stop the scarf from curling but I didn't want the piece to turn into an inflexible and hard plank either. The muslin seems to make the scarf hold its form nicely, but that might just be the vigorous steam blocking that preceded the sewing. I will keep you posted if the lining doesn't work in the long run.
I do love the fabric and the scarf feels actually really nice now that it's lined. Alpaca tends to be a bit itchy sometimes so the cotton lining feels much softer against the skin. I actually might line other scarfs in the future, but hopefully those projects will be premeditated and not rescue missions such as this.
I'm just a bit annoyed that fixing the problems with this scarf took me almost as long as knitting the whole thing altogether. Crochet is not my forte and neither is sewing. The overcast stitch lining alone took me hours to sew. I just feel I wasted a lot of time I could have spent in a million more productive ways.