Independence is a tough route. Made tougher with BYU joining the Big12. But not impossible if it maximizes the $. If a Pac12 team were to go the independent route they would need to set up a scheduling agreement with the Big12, SEC or Big10. Similar to ND playing 5 ACC teams each season. The SEC would make the most sense because they only play 8 conference games today.
For Olympic Sports the Pac12 teams could ask to join the MWC, WCC, etc. No travel issues there. Does it really matter what conference schools are in for water polo, cross-country, rowing, soccer, gymnastics, golf, tennis, etc. etc. Sports like wrestling & hockey seem to do OK morphing together conferences for competition.
Its nice to say that USC, Washington, UCLA, etc don't want to be affiliated with the SEC, but $ talk. If it is the difference between $40M/year & $80/year annually in media rights fees- Pac12 teams will be like rats scrambling off a sinking ship to join the SEC. Heck the Big10 took Nebraska knowing they were getting the boot from the AAU. Nebraska was the best FB brand the Big10 could grab.
Plus it seems like FB & MBB are straying farther & farther from the scholar-athlete mission. There are legal challenges and Title IX issues- money is becoming more important to a modern Athletic Department.