I love the idea that CocoBrynn posted about doing books instead of greeting cards. If that doesn't work out for you or if you still get many greeting cards, I just wanted to offer this suggestion for making ornaments out of them. I did this with some of our wedding cards and now we do them with our Christmas cards every year. They turn out really pretty and have become some of our favorite ornaments.
Here are some simple directions: https://www.ehow.com/how_5310737_make-out-recycled-christmas-cards.html
Re: s/o if you get shower greeting cards
That's a very cool idea. Does it look similar to these?