EDIT: thanks for the update, but I still don’t see the need to remove the card the same way it went in. If you can insert the card in the manual feed of any printer, it’s pulled through and pops out the same, your card is printed. Please, help me to understand why you need it to come out the way it went in.
Perhaps if you told us what your use is, it would help us identify what you need. As is, I can suggest any printer which would have a manual feed tray. You put the card in, hit print, the card is pulled through printed. Next card, repeat.
Are you doing something which has a special need where this wouldn’t work?