Here's what I would do.
Wear the dress blues under the cap and gown and carry my Marine Corps cover.
Once I received the diploma, take off the cap and put on my Marine Corps cover and pull off the gown!
VOILA!
From the Halls of Montezumaaaaa...to the shores of Tripoli!!!
Semper Fi,
Kelly
I'm glad you referred to it being a cover as someone earlier had called it a "top".