I've got a hybrid with a rear rack with a wire basket zip tied to it, and I've used a traditional milk crate on my last bike. They make 1 inch zip straps that are sold at Walmart with strong 100 lb working load strapping and strong metal buckles with spring levers that make great quick release attachments. It's the same sort of straps you would use to secure a tarp covered load on a truck bed, but specifically the smallest and lightest ones. Pack Cam Tie Down Straps Cargo Lash Luggage Nylon Bag Belt Metal Buckle | eBay

I've had great luck with simply lacing paracord between the holes in the basket and the frame of the rack just like a shoe, and then tightening up with a single quick release shoe string knot. The idea is that the more times you wrap the single string around the perimeter of the frame of the rack, the higher ratio of slack in the rope to play in the entire basket. This way you can attach the entire basket with a single knot, and take it off just as easily as you could remove the laces from a shoe, yet hold it securely even if the knots work loose. The play that you do end up with acts as a bit of a shock absorber, so it's not bad at all.

Obviously you have to be careful with loose strings and straps and make sure to secure any excess line to keep it out of wheels, etc. A zip strap or some parachord with basic slip knots, bow line knots, and quick release knots can securely and temporarily secure a rack basket on an odd sized load. Technically you could weave a harness out of parachord for any given load. Something as simple as piece of stick used as a toggle could act as a strong, lightweight, and secure quick release mechanism.