Geometry optimization: dependence on initial geometry
Starting with two moieties, the final "optimized" geometry is not
  unique and depends highly on how they are placed initially. Is there a
  way to avoid this?


Yes and no. No, because, as OP anticipated, starting from an input geometry the optimisation algorithm will indeed find the closest (from the algorihtm point of view) local minimum and not necessarily the global one. And yes, because by performing an extensive conformational analysis, one in principle can find structures that correspond to all possible local minima and then identify the global one.