I often use 1D/2D scheme to model flooding along dammed river and -in general- I have no problem for unsteady solution.
However some problem I noticed that if 2D area is overlapping 1D elements and then I check the model to remove any overlapping faces (next image).
Currently, I did not find a solution me too (but I hope to resolve soon) for stability of 1D/2D model in urban areas where a long lateral structure follow the border of 1D model. In fact, the 1D river is very strict (5meters) and then some points of the 2D area are within the 1D model.
I stay connected to future developments.