Weird as it seems, looks to me like KSU could win the Big 12 North outright, without even needing tie-breakers, and still fail to reach bowl-eligibility. The kicker here is that 6-6 doesn't get the Wildcats to a bowl.
Below I've put one scenario that has the Wildcats going 4-4 in the Big 12, 6-6 overall, and winning the Big 12 North. It doesn't even require really ludicrous upsets. I'm not saying that this is the most likely scenario, but that it's not out of the question for the Wildcats to play in the Big 12 Championship game at 6-6.
KSU: Beats MU, but loses to ku, NU, and OU.
MU: Beats CU, ku, ISU; loses to KSU and BU.
CU: Beats NU and A & M in Boulder; loses to MU, OSU, ISU
NU: Beats KSU and Baylor; loses to CU, OU, ku
ISU: Beats CU; loses to MU, OSU, A & M
ku: Beats KSU and NU; loses to UT, TT, and MU