This is why I like Samorgas, above any other organizer I have tried. They add barely any weight at all to a bag, especially to a canvas bag, and they don't make my Speedy B 30 boxy at all (or my Neverfull). This is for the regular felt organizer, not the double felt. I love my Samorgas, they really enhanced the functionality of my bags.
Does the regular felt hold the structure of your neverfull?