Thanks much Dominique!  There may be a better way for me to have done this since I don't know coding very well, but it seems to be working for the most part.  For anyone else who may face this issue, I defined a variable for my map service of type ArcGISDynamicMapServiceLayer and then found a line of code on another forum to add only visible layers of the service to the LayerIDs value, as follows: 
            ArcGISDynamicMapServiceLayer shorelineAssessmentMapperMapLayer = (ArcGISDynamicMapServiceLayer)ShorelineAssessmentMapperMap.Layers[3];
            ESRI.ArcGIS.Client.Geometry.MapPoint clickPoint = e.MapPoint;
            ESRI.ArcGIS.Client.Tasks.IdentifyParameters identifyParams = new IdentifyParameters()
            {
                Geometry = clickPoint,
                MapExtent = ShorelineAssessmentMapperMap.Extent,
                Width = (int)ShorelineAssessmentMapperMap.ActualWidth,
                Height = (int)ShorelineAssessmentMapperMap.ActualHeight,
                LayerOption = LayerOption.all,
                SpatialReference = ShorelineAssessmentMapperMap.SpatialReference,
            };
            foreach (int x in shorelineAssessmentMapperMapLayer.VisibleLayers)
                identifyParams.LayerIds.Add(x);
            IdentifyTask identifyTask = new IdentifyTask(shorelineAssessmentMapperMapLayer.Url);
            identifyTask.ExecuteCompleted += IdentifyTask_ExecuteCompleted;
            identifyTask.Failed += IdentifyTask_Failed;
            identifyTask.ExecuteAsync(identifyParams);