I haven't done much in the JVS field, so I'm not positive whether this is possible or not.
Instead of using prints, my idea is a JVS object that is only a floating number. These JVS objects have zone-like qualities, and thus can be placed inside another JVS object. When the door is activated, the numbered JVS object moves with the door. Of course, this would require a standardized default rotation speed among all JVS doors. The number would be split in half length-wise, and flipped, so it is shown in the correct orientation on either side of the door.
/discuss or make