You may find requsting the same waitstaff each night in the Haven. Probably a greater chance than in the MDR.
I would suggest making your specialty dinning reservation as soon as possible. You can do this beginning 125 days out. You can select the venue and the time on line. The concierge can usually make changes upon embarkation. He/she can also make your reservations onboard, but there is no real reason to wait.
BTW, there is a on-shore concierge group that can assist you in making special requests prior to your cruise. You can contact them at 855-625-4283 or norwegianconciergedesk@ncl.com. All you need is your booking number. I recommend you call since they may make suggestions about things you might not have thought of.