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The following will work:

# Local Variables:
# org-time-stamp-custom-formats: ("<%Y-%m>" . "<%Y-%m %H:%M>")
# eval: (org-toggle-time-stamp-overlays)
# End:

Using (org-toggle-time-stamp-overlays) (C-cC-xC-t) to ensure they are properly displayed.

You will need to confirm that these are safe local variables for them to apply however once they are approved the document will load with them already showing.

Toggle command referenced from the Org Manual