Add ND and it might pay for stadium expansion at several smaller stadiums. No way would I give up the home game for ND at a neutral site and not get a neutral site back for the away game at ND.
The big item for ND would be travel. And that is why I don't see them joining the Big XII. ND will stay independent and be in the Big East for everything else.
The Big East isn't on the most solid footing either in all of this realignment mess. Keep in mind that the Big XII minus Nebraska and Colorado becomes one of the premier top to bottom basketball conferences in the country. If the SEC raids the ACC like has been mentioned, the Big 10 is definitely interested in a few ACC schools, what happens to the Big East? Bye, bye. Now Notre Dames parking pass in the Big East expires. The Big XII would look pretty damn enticing to them with all of the things I previously mentioned.
As for the neutral site games with ND... ND loves playing neutral site games. maybe every 4 years ISU could host once, travel once, and then they play 2 neutral site games so they each give up a home game? Maybe with the amount of cash ND would stand to make adding the Big XII tv deal proceeds to their bank account they won't mind playing in Ames, Lawrence, or Waco.... Who knows what would grab their interest. I can tell you that if you add ND to the Big XII at 10 teams the stability concerns are substantially less. Think of ND as a counterweight to Texas. The leadership at both schools are buddy/buddy when it comes to athletics so it would make sense.