I have used acrylic, but yeah, whatever ink you want.
I have printed plastisol onto paper, and ran it through the dryer the exact same as a t-shirt with great success. That is what I would do, fire the boxes through the conveyor. {Testing the results to make sure the heat doesn't warp the box, of course. } My project was for my brothers wedding invites. the result was perfect, with the plastisol taking a kind of glossy finish.
Good luck!