OP,
First, Congrats! That's a big deal and so special to have your sister hood you! Welcome to FlyerTalk, but I am sorry for what brought you here. As a fellow academic (the "Dr" in my name is for academia), I feel your Herff Jones pain. If you've not yet filled out the Sixt lost and found form here, do so. Also, you can try there social media contacts. Here's their Linktree.

I don't know much about Sixt itself, but you may have better luck (if you have not tried) finding local Indy folks on Reddit or Facebook. Are you in Indy? It's possible you can just stop by or find someone who is also an alum who will check. The toughest part of these situations is reaching a human. That's what is so frustrating. Those gowns and hoods are quality looking and feeling, so it's unlikely to have been tossed outright (hopefully!).

Mods, any chance this would be better suited in a local forum for Indy? (I am really bad at knowing that aspect so you are probably right having it here, but also I think Sixt is more European focused, despite operating in the US; I know if it, of course, but despite renting cars from all the major players, I think, Sixt has never come up as an option, for no reason I can think of apart from opportunity.)

Congratulations again, OP! And please let us know if you find it! FT is filled with great folks who care and if they can help, they will!