I believe the NR drawing deadline is March 15 prior to the season for that year.They now have the super tags also where you can increase your chances for a certain tag like moose or sheep for $5 per try.
We buy our tags over the counter except for moose,sheep,antelope,bison,mountain goat and certain area elk and deer hunts.Not exactly sure how the drawings are held for NR.
Here is the FWP website fwp.mt.gov
Elkshed