Hello,
I have the Chicco travel system and you can put them on top of the shopping cart. You should have an orange groove under the car seat and that is where I put that side of the car seat on the grocery cart. I know that it still moves around, but this is my second child with the travel system and the car seat has not fallen into the cart or off the cart. I go over the bumps even at the beginning of the store and think that for sure it will fall, but it never has.
I felt the same way with my first child and would try to hold the car seat, but after some time I became confident that it wouldn't fall. You are right though it really isn't made for the grocery cart, the only cart that I have found that it really fits is at Babies R Us. I bought the travel system there and they told me about the grocery cart thing.
Hope this helps and if you have more questions let me know.
B.