I find odd the idea of sleeping directly on the mattress. Seems to me a regular bag with full length zipper can be used just as well as a quilt when open, but you can also have the draft-free warmth when you need it and the comfort of sleeping on something other that rubber.
There are wide or rectangular bags that are much less confining than a mummy.
I've always used a liner in a sleeping bag which can be used by itself and is easy to wash (make them myself and they stay in place with velcro).