My grandfather used to have a jam/juice-making tool that was used with a bag like that. Basically, it was two long oak "paddles", about 4 inches tall and maybe 24 inches long, I'd guess, hinged at the end with a canvas hinge...we'd pick massive quantities of grapes or blackberries, then he'd use the "squeezer" to crush the berries or grapes, and the juice would run out of the hanging bag and into the catch kettle...it worked great. We would "spin the bag", and he'd squeeze the lower part of the bag, repeatedly.
Every other summer we'd make home-canned blackberry juice, which is one heck of a drink, and home-canned grape juice, which is, well...grape juice. THis was back when the local wineries were JUST getting started, and their grapes were not deemed good enough for making wine from. We'd go to a couple local vineyards and bring home literally gunnysacks filled with grapes!
Your cloth bang and hanging setup really reminded me of the old days! I had not thought of that memory set for a long, long time!