How interesting. My Guild just had a program on antique quilts. Alma Moates was the speaker and she described her grandmother peeling batting off of paper straight from the cotton gin it was on wide rolls. At one point she visited a Gin and was shown a part of the machine where stray fibers were blown onto the paper. It wasn't the main line of cotton just a way to catch the stray fibers. It could be then rolled and used as batting. If you Grandfather had a gin maybe it was the same for your grandmothers. Sometimes real cotton was used and was considered, wadding. You could try to "comb" the cotton between two wire brushes to straighten the fibers.