EXACT positioning sounds exactly what you want to do. The picture will
not move if text is added above, below, or on top of it.

Simply right click on the image after inserting it.  Once done click on
Format Picture in the dropdown list.  Then click on the Layout tab.  Click
on None under Wrapping Style.  While this will NOT restrict you from moving
the image manually on the page by clicking and dragging, it will prevent
text from shifting the position of the image.

You would then need to set the "front to back" sequence of any overlay.