I have done several quilts using the birthing method. I think your plan will work. I don't hang on the clothesline I just spread it out on the floor.
Once I turned it right side out I sewed very close to the edge all of the way around. That seemed to help it lay flat
I would be afraid if you didn't sew the front and back together at all it would "floppy" But that's how those tie fleece blankets are and a lot of people like them
I don't know how just tacking will work - I guess it depends on how often. When I did this I did quilt in cross hatches about 8" apart and everything went just fine
good luck