I use the fencing cylinders, lined with feed bags too....but I set it up so I can unhook the fencing and open it up to shovel out.(drooling) Oh do I ever want a compost setup like that one. I think I'm going to ask for someone to build it for me for Christmas.
Currently I use 10' lengths of 4' tall rabbit-proof (?) fencing wire formed into circles. (It's the stuff with the closer mesh at the bottom.) I line it with cardboard to stop the contents spilling out and to keep the moisture in. Works great for the actual composting, but it's horrible for turning the compost as you have to reach down inside the circle - a killer for the aging, aching back.
You could line the chain link too?