I sleep on my side and have to turn pretty constantly or I will be stiff and sore in the morning, even on a comfy bed.
I think quilts can work for this type of sleeper plenty well. I make my quilts just a bit wider, about 50" at the widest point, to help work with this. I have also found that actually using the little straps under it. If it is warmer out, I don't worry about this, but as I push the limits of my quilt more, I will put them on and it helps a good bit. Especially using one around my hips area.
The guide I wrote for my quilt has these features, and they work very well for me.
I think that giving a quilt a try would be a good decision if you are unhappy with mummy bags.