Buy a cart cover. They usually have a belt included. Or I'm sure that someone out there sells belts for the carts. Alternately, use the harness. I'd put it on him around the house so he gets used to it and you find out if you need to add duct tape to the buckles or something. You can also work on him at home to come to you, stay with you, and not run when you are out of the house. When he stops, you praise him. When he runs off, you go after him, stop him and tell him to stay with you.
It has happened to most parents. My DD ran out of Staples when she was a little under 2 and was on the sidewalk before I caught her. If she can't stay with me, she goes in the stroller or in the cart.
You can also try PeaPod or your local equivalent. PeaPod is fairly cheap for the delivery.
You also have a manny, right? Does the manny have trouble wrangling him. If not, what does he do differently? Does your son run as much for anyone else or just you? You might need to take notes from others.