No, I think TnT is correct. I was going by what was written in the game manual, which is not that clear. But the math doesn't add up.
If the NBBA now has 2 auto-relegated teams and 3 relegation series (5 vs 7, 5 vs 7. 6 vs 6). then there will only be 5 open spots. 4 league winners plus 1. So the best team record that doesn't win a league in all of II makes sense. The manual could be way more clear on this.
So with 16 III leagues into 4 II leagues there are 4 extra record based promotion spots there then (5 series x 4 leagues = 20, with 16 league winners).
Sorry Bullets, didn't mean to get your hopes up

Still have a shot to promote based on record but no guarantees....