Montana has 7 appearances in the FCS Championship game (1995, 1996, 2000, 2001, 2004, 2008, 2009) resulting in 2 national championships (1995 and 2001). 

NDSU not only has 4 consecutive FCS Championships, but has been in the FCS playoffs every year but 2 since becoming eligble. (They went 10-1 and were ranked in the top 10 in polling during their last two years of reclassification from Div II before becoming eligible for the playoffs.) Speaking of Div II, from Wikipedia:

North Dakota State appeared in 23 NCAA Division II Playoff Berth's from 1964 to 2003. During this stretch NDSU compiled a massive 347-94-4 winning almost 80% of their games for 4 decades and claiming 8 Championships along the way. NDSU appeared in 7 out of 10 Championship games from 1981-1990; including appearing in 5 straight Championship games, an unrivaled number in DII as they posted an astounding 111-16-2(.875) mark from 1981-1990. While this is a startling record, from 1964 to 1973 the Bison went 90-12-1(.887) which included a 35 game unbeaten streak.

I think NDSU and BYU would be great additions to the Big XII. With all the oil money in North Dakota, they could quickly upgrade their facilities and I think they would be competative.