Would this idea help. Cut 2 strips of fabric about 50"x 18" and stitch them together at the middle. Then sew each end to your 'inner tube' to make a square seat. If you wanted to wrap the fabric around the tube you would need the strips to be at least another 45" longer.
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I might be a bit concerned about the foam beans though as they have a habit of moving around. Could you make a sleeve and use a couple of noodles instead.