To be honest, you do not necessarily need a double-register to play well.The Saxist said:
For instance, I am able to play an Artley plastic bass clarinet throughout the whole range. It took a lot of practice in order to achieve this.
However, an easier solution may be to get a Grabner, or a Fobes mouthpiece. After I received my Grabner LB, it made playing all the bass clarinet notes seem ridiculously easy.