You should be using the static_layer plugin for the move_base Local Costmap, and it should be the first layer.
You must provide accurate frame_id info so that the spatial relationship between your data and the (global) map frame can be determined. Assuming you have rolling_window
set to true, the local costmap code will use the robot's current map x,y position (not pose!) and the costmap dimensions to select a small region from yourthe larger-dimension grid data map you provide.