As for attaching something less stretchy to the top? Stretch the covers to match, and then sew it on
Put them ON and pin (carefully) Do not just guess.
I've only done it twice (needed a vinyl trim on spandex) and the pinning phase is very persnickety. Put them on, pin, walk around for a minute. Take them off and go do something else for thirty minutes. Come back and put them on, walk a couple laps of the house.
My trial and error resulted in having to pin the vinyl almost uncomfortably tight in order to not slide down when wearing and walking. Where yours sits on your body will affect this.