I'd be careful about saying scratch Notre Dame.
If they ever want to win again they need to recruit Texas like they were doing in the 80's and early 90's. The last successful coach there was straight out of Texas for that very reason. They can always recruit Midwest and East coast Catholic kids but Texas kids are where they are lacking.
I'd agree the Big 12 would have to agree to a sweetheart deal for them that was basically what they gave Texas. Under that deal Notre Dame could STILL have it's own network which net even more than the estimated 3-5 mil per for Texas.
LSU is a real long shot to be sure.
Possibilities imho:
Air Force --- Nice service academy without being too far away, replaces Colorado in same market.
Arkansas --- they suffer without Texas/OU ties for recruiting and rivalries.
Rice --- Academic school and football fodder for the Big 12 South in a 14 team alignment plus insanely easy travel.