I had a similar problem with a screw at a sawdust stocker bin outfeed. There was originaly 3 different pitches on that screw and that was not enough to avoid plugging even if there was variable speed drive on. The original diameter was 24" an the 3 pitches 12"-18"-24". The actual screw is still 24" diametre but has a progressive pitch on full length and that why it's working at 90% loading. There is something more to be carefull: The position of the hopper vs the rotation sens of the screw. You have to make an arrangement to be sure that the screw is not lifting the material.
It can be a good idea to put a shaftless screw. Those screws are developped for very hard applications. Actualy, i do not have experiences with those one, but i expect to use some in a new pond design.