Hello,
A supercritical flow at an entrance needs to prescribe velocity AND depth, as says the error message, this is the theory and you cannot escape it, you must know the depth. This would be the first thing to try.
A solid discharge in the middle of the domain is possible with DredgeSim, however I see nobody using it so we do not have too much experience with it.
Maybe my colleagues in charge of sediment transport will have other ideas regarding what to do with the sediment.
With best regards,
Jean-Michel Hervouet