Hello,
I don't think that changing the turbulence model or the eddy viscosity will give you much other results.
You said that in the experimental test there was uniform flow regime. This means that your prescribed water level at the outlet must correspond to the normal depth.
I can only advise to calculate, based on the roughness, width and slope, the normal depth, the critical depth, and using the Bernoulli equation along with your boundary conditions also the water surface line. This will maybe bring some insights into your model.
Hope this helps,
Clemens