So...after some trial and error I finally decided that my favorite solution was to have the cover roll up ( keeping the inside clean) and securing it with elastic straps. This allows you to use the seat belt (now included with the cover) as a carrying handle.
I like this version for several reasons:
*The included seat belt can be washed to keep it clean instead of using the one in the cart.
*The cover rolls into itself so the inside part that baby sits on stays clean.
*The elastic straps make it really simple and really quick to roll it up and secure.
So far the response has been really great! I think this design will be around for quite awhile.