It looks like attempting a lateral structure to an off line storage area was a good approach. Unless there is a significant lake in line with the system, it makes sense to go with one structure rather than two. You tried the lateral structure with a single reach, right?
In the unsteady flow analysis window, take a look into Options>Calculation Options and Tolerances. There are inline and lateral structure flow stability factors you can turn up. They dampen the calculation of flow over the structure. That can help stability. There is also a number of iterations that can be increased. The default is a single calculation, which may be way off. Try iterating the 1D/2D flow calculation (within each unsteady iteration). There is also a minimum flow tolerance, which allows those iterations to cut off at a reasonably low value. It is different for each model.
Consider how much storage is available in the storage area, and whether the water surface elevation would shoot up rapidly in a single time step. Was the extrapolation warning because the water surface was unreasonable?