After a couple of false starts, I ended up with an accordion pop-up card, taken from Helen Hiebert's fabulous guide, Playing with Pop-ups. Here are 3 of the cards, shown from above.
The "thank you" is on the inside popups -- once in English and once in Italian. The outside popup says "Happy 2017." To add visual interest, I grabbed an assortment of fonts from old Wired magazines.
On the front and back, I pasted small photos from an old college yearbook.
But I forgot one thing -- space to write a personal message! To fix this, I made another card that holds the popup, enclosed in a small handmade envelope. There's space on the back to write.