Then you aren't trying hard enough. That's what they would do. They will not join the Big East. It's zero chance. I think too many of you people have misperceptions about the school, the region and the Big East. As someone who arrived on the KU campus from Connecticut as a UConn grad in 1991, I think I have perhaps a more realistic perspective.
1. Take a B1G invite if it comes
2. Stay in Big 12, backfill two spots with Cinci and Houston.
3. If more schools leave (unlikely unless #1 happens) then explore the Pac, which would take KU without much deliberation, possibly with OK State.
Somewhere around option 18 is "join the Big East", just before "disband the AD".