You could do something like a knitted version of a 'quillow' (lots of patts for those online). You could then incorporate or attach handles to the pillow portion. You'd carry the afghan in what looked like a tote. Seems like it'd be easy enough to do (as I see it in my head!).
Is that along the lines of what you had in mind?
ETA: found patt for knitted quillow linked on Rav