Is there an accurate way to place an AutoCAD clipboard object into the current drawing?

Yes, of course there is.  If you use the Ctrl+C option, to copy objects to the clipboard, those clipboard object(s) will have the lower left-hand corner of their extents as the base point.  This may not be the right spot every time.  Use the keyboard shortcut of Ctrl+Shft+C to pick a base point for your clipboard object, then paste to the accurate point in the destination AutoCAD file.