I doubt it's Stanford. The dates don't line up. Also, NPHC groups generally hold their own recruitment events; interested people choose the one NPHC org they want to pursue, and typically attend rush events just for that one org.
You could squeeze in a 6-week NM period before spring finals. Most, if not all, NPC orgs have adopted NM periods of 6-8 weeks. Still, juggling NM obligations, late-semester academic work, other activities, a social life, and sleep (!) would be tough.
Anyway... good luck, sundance. Have fun.