In first example using current format, ND or another Independent ranked #1 would be seeded #5 and 4 Conference Champs would be seeded 1-4 and get the coveted first round bye.
Standard 12 Team Playoff
.....R1.........R2......R3
12 @5 => 4 => W1
11 @6 => 3 => W2
10 @7 => 2
9 @8 => 1
In the second example an Independent team is ranked #1 and seeded #1, but does not get a first round bye (to prevent scenario where IND team could win NC playing only 15 games vs Conf teams playing 16-17 games). The 4 byes slide down to the 4 Conference Champs (seeds 2-5 in this example).
Under this scenario, the #1 seeded IND team would play at home in round 1 vs the #12 seed. The winner of this game would advance to the second round in the 1 seed bracket and would play a neutral site game vs the round 1 winner between the 8 and 9 seed.
The winner of this game would advance to the third round in the 1 seed bracket and would play a neutral site game vs the round 2 winner between the 4 and 5 seed.
Alt Version (An IND team #1-4)
.......R1.................R2........R3
12 @IND#1 | 5 vs 4 => W1
11 @6 => 3 => W2
10 @7 => 2
9 @8 => IND#1
***Note: while this would be a significant change for an Independent seeded 1-3, for an Independent seeded 4 it would be semantics only as an Independent seeded 4th or 5th would have identical playoff paths.