Keeping in mind that priorities include things like spreading the "new" teams around, ease of transition after Texas/Oklahoma leave, competitive balance, geography, access to Texas recruiting, rivalries, etc.

Option 1 (from article):
North: Cincinnati, BYU, Iowa State, Kansas, Kansas State, Oklahoma, Oklahoma State
South: Baylor, Houston, TCU, Texas, Texas Tech, UCF, West Virginia
----balances new teams, easy transition, good competitive balance, but bad geography and Texas access

Option 2 (modified from article):
North: North: Cincinnati, West Virginia, BYU, Iowa State, Kansas, Kansas State, Oklahoma
South: Baylor, Houston, TCU, Texas, Texas Tech, UCF, Oklahoma St
----balances new teams, easy transition, a little worse competitive balance with OK St and Baylor in same div, but better geography (pretty great except for bad for BYU). Texas access is still bad and Oklahoma/OK St rivalry is hurt

Option 3 (East/West):
West: BYU, Texas Tech, Texas, TCU, Baylor, Houston, Oklahoma St
East: Oklahoma, Cincy, West Virginia, UCF, Iowa St, Kansas, Kansas St
----balances new teams, easy transition, better geography, but still has issues with competitive balance, Texas access (though here we benefit) and takes Oklahoma/Oklahoma St rivalry away

Option 4 (Split Texas):
West: BYU, Texas Tech, TCU, Oklahoma, Oklahoma St, Kansas, Kansas St
East: Texas, Houston, Baylor, UCF, Iowa St, Cincy, West Virginia
----good competitive balance and ease of transition, gives everyone access to Texas recruiting. Geography mostly good (a bit awkward for Iowa St), but doesn't split new teams equally

Option 4B (Option 4 with follow-on plan):
As outlined in Option 4, but with the plan that when Texas/Oklahoma leave, send TCU East and add SDSU, Boise, UNLV to West, and Memphis to East resulting in
West: SDSU/UNLV, Kansas/Kansas St, BYU/Boise, Texas Tech/Oklahoma St
East: Iowa St/Memphis, UCF/Houston, TCU/Baylor, Cincy/WVU
---balances "new" teams, geography and competitive balance, opens new fertile recruiting areas (California and LV) while making Big 12 a coast-to-coast conference with representation in every time zone, but requires swapping one program (TCU) while adding more G5 teams