Do you what the Champions League is? It's the top teams from all the leagues in Europe.
If the NCAA said the Champions League games would be exempt each year and the conferences got the TV money from whomever bought the rights to the NCAA basketball Champions League then it could work. There are 32 conferences you give each conference 1 bid and then the more successful conferences would get more of the 32 other slots like the UEFA Champions League which cap 4 slots for the best league La Liga, BPL, Bundesliga.
So you would get 32 teams, then each of these conferences would get an additional ACC-3 B1G-3, PAC-3, Big XII-3, MWC-3, SEC-3, AAC-2, A-10-2, Big East-2, Missouri Valley-1, and give out the remaining 7 slots to the lower conferences.
You draw the 64 teams into 16 regions. You seed them 1-64 regardless of conferences and keep the top 16 apart. Play the 3 teams you are drawn into home/home. The group winner goes on, tiebreakers are head to head/if that doesn't decide the higher seed advances.
From there you get the 16 remaining teams and draw matchups, the highest 8 get home-court. Then your down to 8 and so-on.
Again, these games would have to be sprinkled in during the regular season from November till before March and the conference tournaments. It would affect 64 of the 320+ NCAA teams each year, but it would generate a crapload of money and would get fun matchups. The winning team would play 9 additional games during the season, and participating teams would play only a minimum of 6 more games under my format.