Im questioning your characterization and the over-importance you are attaching to the quote. You are implying that EVERY council father agreed with this. Maybe it was only 2, or maybe it was 10 - it's not clear. Even if it was everyone there, that means nothing - because the cardinals are not infallible without the pope. So, as you admitted, this is not authoritative, therefore it's on the same level of theological opinion as Bellarmine vs Cajetan, etc.
If you actually read the excerpt from the book, you would see that Archbishop Purcell was speaking to the
whole Council about questions/concerns he had regarding infallibility. When he relays the question asked and answered at the council regarding what happens when a pope becomes a heretic, he never mentions that anyone disagreed with it. Given the answer to this question was critical for him in accepting papal infallibility, I am sure that if there were any different/contrary answers, he would have at least mentioned them.
To be clear, the only importance I am lending it is that it was discussed at the Council and there was no argument made against it. When the issue of a heretical pope came up, the Council used Bellarmine's teaching to assuage another Father's concerns. For me, this is just another indication that it is Bellarmine's teachings that the Church looked to in these matters.
When I look at the "evidence" Bellarmine stands above the rest of the theologians on this matter. If others want to look to other theologians, I guess that's their prerogative, but I am sick of the anti-sede rhetoric (you know the rhetoric that says stuff like "Outside Bellarmine there is no Salvation"?) that sedes are wrong for not giving equal credence to them and that we should HAVE TO DO SO. No, I don't have to do so and so far no one has given me any reason to believe that their teaching is heavier or more correct than Bellarmine's.
I think I have said enough on this matter. Carry on.