It appears to me that your pic only shows the finish welt from the outside. The plastic is on the reverse side, and sewn in along with the welt. It tucks up under the drape and secures the leading edge to the scuttle, (at least, this is how this top was installed). I see no other method for securing the top and have good reason to believe that this top was original, (one being only 54,000M and kept in dry storage). Perhaps my 1st pic wasn't clear enough, so I'm posting another. The material is discolored and opaque, and appears to be the same or similar to the rear window, two strips, sandwiched together.
Since my 1st post, the top manufacturer is refusing to take the top back. Estimates to modify are averaging $250!