The quasi-steady model does not solve the backwater equation. If there is no convergence in the first time step is because the initial condition is not accurate enough. 

Sorry, I meant the steady model doesn't start (I keep up mixing up the definitions of the models). Unsteady model and quasi-steady model (with same initial conditions as for the steady model) do start.

Bijzonder... The steady model should be the most robust one, as it solved an ODE, contrary to the quasi-steady and unsteady, which solve a PDE. The flow initial condition is irrelevant in the case of the steady model. Only the initial bed level and the downstream flow boundary condition matter. I guess there is an issue with the downstream boundary condition. What are you imposing? Copy paste the log-file that the model generates. 

Hi Hermjan, 
There are several backwater solvers which vary in accuracy (1st or 4th order) and in variable solved (energy or flow depth). There are some minor details for chosing one or another one, but all of them should provide you with a good solution. The fact that a solution is not found is a symptom that a hypothesis underlying the application of a backwater solver is not fullfiled. 
Concerning theta in the quasi-steady and unsteady solvers. The system of equations solved is fundamentally different in each case. Essentially, one has two unkonws in space and one in time and the other only one in time and two in space. Hence, the numerical scheme that solves one system of equations does not need to be valid to solve the other one. In particular, a fully implicit time integration is required for the quasi-steady scheme to be stable, while the unsteady scheme is stable with half implicit half explicit and one gains a second order accuracy. 
Before running a morphodynamic simulation, I would test that the hydrodynamics are correct. To this end, I would recommend you to conduct a convergence study. Simply decrease the grid size and check whether the solution converges. This will also tell you how fast does it converge (i.e., order of accuracy) and it is an essential step to firmly decide on the necessary space step for your simulation. Furthermore, I would recommend that you compare with an analytical solution such as the propagation of a Gaussian flood wave. Once the hydrodynamics are clear and beyond doubt, next step is including morphodynamics. Otherwise, one is never sure if the results are genuine or the spurious due to poor numerics.