possibly more importantly, are there any flags netsuite sets to indicate that these fulfillments have had their packing slip printed?

Is there is a similar IF System Notes to what appears on Sales Orders with the system notes showing Print Picking Ticket = T/F. Maybe look on the IF System Notes for a clue. Also this SA migth be helpful https://netsuite.custhelp.com/app/answers/detail/a_id/81667