This was my first event, so I didn't realize the exchange station closed completely after it was over; I thought only the Kami became unavailable. As that is not the case , apparently, what do I do with the 54 cat's eyes I have? Will the event come around again?

Ouch, sorry to hear that. I'm afraid there will probably be no future use for your Cat's Eyes, seeing as no Kami event has ever been repeated (with the exception of the Hoppers around Easter), unless perhaps you're able to find someone who'd buy them as retired collector's items. 

go to the item exchange and type in cat's for items you have .A few things can be baught for them still