External access to our development environment is forbidden so I can't provide a testable example for you.
Opening up the DOCX file word/_rels/document.xml.rels shows the embedded JPG files saved with a .php extension. If I manually change .php to .jpg then the embedded images appear. (Rename the .docx as a .zip, navigate to the appropriate component, copy that to the desktop, edit it on the desktop, copy it back by overwriting, rename the file back as a .docx)
The headers we're sending should be correct. What headers do you send with your minimal example for the streamed image? Is there a URL I can use so I can compare your headers against ours?