Payne's view causes the passage to lose logical flow

Three problems: (1) Paul never once mentions cloth coverings in vv.3-14 on Payne's view, but suddenly in v.15 introduces the concept. (2) Payne thinks women weren't wearing cloth coverings, so why mention them in v.15? (3) The natural reading of the whole passage flips in the last verse -- much of the passage becomes pointless if v.15 is all you needed. How many verses could you erase?