Unlike most other organizations NSA has their rulebook online. See
http://www.playnsa.com.
Rule 8-5-f states a runner receives two bases from the last base occupied. In your scenario (ball thrown into dead ball territory and R1 between 1st and 2nd at time of throw) R1 would be awarded 3rd base.
Remember that if the ball was a caught fly ball, R1 would still be required to go back and touch first, then touch second before legally occupying third.