my quilts don't have straps.

I don't have too many issues with draftiness, either. I seem to have practiced enough with a 20" mattress and a quilt that I sleep quite warmly, into the low 20F range with appropriate base layer and a warm beanie hat.

I sleep directly on the pad - NeoAir or Big Agnes Q Core - and the base layer does the job nicely of limiting the issue of skin-on-nylon.