+Fellay characterizes the Conciliar Church as NOT being a brand new religion but being substantially Catholic, with some some problems that need to be fixed.
To be fair, +Fellay changes his opinion based on the audience. So he holds the above when talking to pro-new-rome people, but he will quote +ABL when talking to true Trads.

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Again, this distinction is very much in line with sedeprivationism. This "historical and structural continuity [with] the True Church" is precisely what sedeprivationism refers to as the "material" Church.
I agree. Fr Wathen was very clear that he was against sedevacantism, 1) because none us has authority to decide, 2) it's a distraction from our daily duties to God. I don't know if Fr was ever confronted with the term 'sedeprivationism'; I would think he would agree with it (as he obviously believed its details). But he always seemed more concentrated on dealing with the Great Conspiracy, which affects ALL aspects of society (the Church, politics, society, the economy etc), much more than just the papal question.