If all of the flow is going into the storage area, you can directly connect the end of the reach, that has the lidded cross sections, directly to the storage area and avoid using the lateral structure.
If you have flow over the lateral structure when you shouldn’t, it sounds like the weir elevation of the lateral structure needs to be increased. The weir elevation needs to be above the energy grade line or else you can get flow. Even if you select water surface on the lateral structure, it still needs to be above the hydraulic grade line if you don’t want flow over it.