My first thought is that the bag (unless you have slept in it already at those temps) maybe not as good quality as you think...draft collar/hood is pretty standard on any mummy type bag.

My son sleeps with a throw fleece, which is about 1/3 + smaller than the average fleece blanket or liner. At anything lower than 20 F or so we both sleep w a loose balaclava hood.

Any piece of fleece clothing probably is the most sensible as you are already bringing it along, weight and size wise.