Ah! I think I get it! And just to clarify... say, my PID%6 = a stat on the hexagon that is not tied with the max - in this case, I continue moving clockwise on the hexagon until I hit the first stat that ties with the max. Otherwise, if the PID%6 = a stat that ties with the max already, the characteristic will represent it.
I.e., with the 30/31/30/31/31/31 spread you used, if PID%6 = 4, then the characteristic will relate to Sp. Attack (Mischievous)... but, if PID%6 = 0 or 1, then the characteristic will relate to Attack (Likes to thrash about).
(Thanks for all of your help - this will significantly improve my roamer RNGing, which has been a pain for the past 48 hrs.)