So, I can be "quiet" about the ligature and to make work Dukoff back again for me, have to concentrate on reeds.no two mouthpieces have the same shaft size, in any size of saxophones, cork is still used precisely for that reason because it can accommodate different sizes and , if not, being filed to size.
The ligature you have on the right is a ligature that comes form Gemany/Bohemia was used on many saxophones, I don't think it is original to you mouthpiece and actually is rather sought after by some people.
The arcives have , I think , the answer to yor question about the ligature
What I found, it may be like a racing car (power wise) or like a "soft" luxury car. Very interesting to experiment.
Thank you very much for short and such a comprehensive answer.