There's a difference between "wanting into the Big 10" and "wanting out of the Big 12".
If you want out of the Big 12, you'll go anywhere. If you just want into the Big 10, you'll probably stay in the Big 12 unless offered by the Big 10. I think that's where Missouri is. They want into the Big 10, but they don't want out of the Big 12 at all cost.
Mizzou may want into the Big 10, but that becomes nearly impossible if they sign onto the Big 12's new handcuffs (6-year TV rights).
I hope Deaton is being sincere when he says Mizzou wants to stay in the Big 12. I'm pretty sure the Big 12's contract with Fox will be voided if Mizzou leaves. You can't replace Mizzou with any of the other programs that are being mentioned. KC and St. Louis are Top 30 TV markets.
The threat of lawsuits is probably the best thing the Big 12 has going for it right now. I would think they could reach some agreement with the SEC to drop any and all lawsuits against them or Texas A&M as long as the SEC agrees to stop poaching schools from the Big 12.