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Father Chazal without hesitation states that Berogoglio is without a doubt a manifest heretic.  He merely adopts the position, against +Bellarmine, that manifest heretics need to be deposed.  He repeatedly stated that he had to "agree with the sedevacantists" about this.

No, the part you miss, Sean, is that Father Chazal states that this heretical pope has no authority, is impounded, and needs to be categorically ignored.  That lack of authority is the sedeprivationist equivalent of ceasing to be Pope formally, while retaining material office.  Father Chazal repeatedly used language like he sits there in the chair and wears white but has no authority.  That's very closely akin to sedeprivationism despite his denials.  He denounces SP in his book because it's a knee-jerk reaction, but when you analyze his position it's nearly identical.  SSPX and former SSPX have been brainwashed into regarding SV as this nasty boogeyman that must be avoided at all costs so he feels obligated to reject it in so many words, despite actually articulating principles very much akin to SP.  SP, by the way, is not SV ... despite the fact that +Sanborn has spun it that way because he only reluctantly accepted SP because +McKenna would not consecrate him otherwise.  But after his consecration he started peddling a flavor of SP that was more SV than it was true SP.

Classical R&R holds that the Pope has formal authority and must be obeyed in all things that do not run contrary to faith or morals, but can and must be resisted in those things that do.

Father Chazal's position is closer to SP than to classical R&R.