I moved to a 20F quilt in 2008 to save weight. I started using it in the spring so I was use to it by the time fall hit. I enjoyed using it enough that I bought a second lighter 40F quilt. I find that quilts are more flexible to use then a confining sleeping bag. I just finally sold off my 3 down sleeping bags as I've realized that I'm never going back to a sleeping bag again.
As some mentioned, it may take some getting use to sleeping directly on a sleeping bad since there is no fabric under you. As I normally sleep in lightweight thermal underware, it's not a problem. But on the occasion, I sleep in my underwear and a t-shirt, sleeping on a foam pad doesn't really bother me.
Drafts aren't a big problem for me as I've trained myself to retuck everytime I flip over to my other side (side sleeper). I don't really toss and turn in my sleep. I do partially wake up and flip myself onto my other side when I do. Unless you have a narrow quilt, there is plenty of material to tuck around your body.
I use a balaclava when I go to sleep. If it's warm, I use it as a pillow case on my stuff sack that acts as my pillow. I wear it when it's cold. If it's really cold, I pull it down all the way so it covers my face and neck and I tend to bunch the quilt around my head but keeping my face exposed so I don't put moisture into the bag. Works for me down into the teens. But I'm a side sleeper which is a warmer way of sleeping then on the back which I suspect would be an issue in a hammock. For most, a down hood that many company's make would be a good replacement for the mummy hood.
Next time you go camping, keep your sleeping bag unzipped and turned sideways and just use it like it's a quilt. It won't fit around you as nicely as a quilt, but it will be close. See how you like it.