Nice take on Papers Please mechanic!
I wasn't able to use the additional stamps when I got them. Also, when a stamp is over an enveloppe and you try to get the stamp, you get the enveloppe instead: I guess there is a Z index priority issue.
Just a few tips for immersion, I would add some background noise, like people chatter or something, and sounds when you make a mistake (I still remember Paper's Please old printer sound!) and some paper sound when the enveloppe arrives on your table and then when you drop it.
Also having the stamps have a slight random rotation to give it a more human way of using stamps, not being always perfectly aligned.
Had fun playing!