If there are co-champions, the BigXII should field a team consisting of champion players from the various co-champion teams. Thereby, the BigXII would field a "one true champion" caliber team. I don't see how this couldn't work and it would totally be within the legal bounds set by the BigXII "one true champion" mindset.
I know what you guys are thinking.
I should be the freakin' BigXII commissioner.