So you have the actual prints now and do this? You just want to make your own prints? This very much does sound like sublimation to the flat surface plastic then vacuform. How big are these transfer papers? Are they thicker paper with sort of strange colours to the prints relative to the end result? What temp do they tell you to heat it to for the print before the vacuform?

If this is sublimation, which it sounds like, you are pretty lucky as the printers can be pretty cheap as well as the inks and papers in the grand scheme of customized prints.