Teams we have never met during the season as non-conference opponents - only in bowl games:
Arkansas 0-1 1964 Cotton
Clemson 1-1 2008 Gator, 1981 Orange
Duke 0-1 1954 Orange
Florida 2-0 1974 Sugar, 1995 Fiesta
Georgia 2-1 1969 Sun, 2014 Gator, 2012 Capital One
Georgia Tech 0-1 1990 Citrus
Houston 0-1 1979 Cotton
Mississippi 0-1 2002 Independence
Mississippi St 1-0 1980 Sun
North Carolina 1-0 1977 Liberty
Stanford 0-1 1940 Rose
Tennessee 2-1 1997 Orange, 1999 Fiesta, 2016 Music City
Besides pulling even with those teams that have scoreboard on us, I would want to play Clemson because they cost us the national championship in 1981 and Arkansas because it would have been us, and not the Razorbacks, with the legitimate claim to the 1964 national championship - which went to Alabama despite the Tide having lost in the Orange Bowl