Attacking the Church is a double-edged sword, on one side the Church was historically the biggest obstacle in the establishing of a totalitarian society, because it shares a lot of similarities with Party structures while propagating ideas outside of what the Party wants, while being so radicated that it's almost untouchable. Using the new, indoctrinated generation to finally attack them has a sense from a totalitarian POV. But on the other side, this is probably the point of fracture with Brazil, since Integralism is based on a Catholic society, and this attack to the Church is probably a step too far for Salgado and the whole Integralist leadership. This risks to bring Brazil into the US-UK camp (at least, in an agreement of "the enemy of my enemy is my friend"), and in joining the embargo of Europe, which would be a disaster for Germany.
Inside the Linz Pakt, I fully agree on how this is going to be a point of fracture with the South, especially Spain, but I don't fully agree on Italy's response. Mussolini was an atheist, and fascism didn't have clerical undertones. The situation of the Church in Fascist Italy was quite similar to the one in Nazi Germany, with an aspiring totalitarian state forced to compromise with the Church and allow it to be a parallel society, alternative to the Party one. I have the impression that the Church and the state-church compromise in Italy was stronger that in Germany, so something like the 1957 purge would be difficult in Italy still, and a lot of young people would still grow up faithful Catholics, with Catholic principia, but I'm not fully convinced the Fascist state would publicly stand for the German Catholic Church and privately not approve.
The point of fracture between Italy and Germany IMO would be more in the early propaganda you mentioned to educate European society to reject American consumerism to aid autarky. The general thing is not a problem, autarky was a term first brought into the forefront of politics by Mussolini himself and Fascist Italy has generally tried to do so in a way. The problem is, how you mentioned, this continental project of social engineering is based solely on German and Nazi sensibilities and culture, with Latin countries being more alienated. Italy would want to walk its own direction on this. And then there's the whole fact that Italy sees itself as a peer and an independent ally of Germany, and it's probably the only state in the Pakt to do so, while Germany, I seem to understand, treats it just as just a bit more than the other members, an auxiliary of the German Empire.
I don't remember if you already had a section on Fascist Italy and what happened in it so I'm not really referring to you or your work in any way, but I want to add a personal note on it: a lot of Nazi victory TLs treat Italian Fascism as a softer partner for Berlin, a more "normal" dictatorship in the Nazi bloc. It was not. Fascism was a totalitarian ideology, in the exact same way Nazism is. Hell, Mussolini literally invented the concept of totalitarianism. The fascist regime wanted to rebuild Italian society in its image, it wanted to create a New Man, a Fascist man. The reasons it's perceived as so different and maybe "tamer" than Nazism are its much reduced exterminationism and the fact that the cultural superstructures it developed on were the ones of a people "warmer" and less bureaucratic than Germans, giving it less of the IMO most uncanny and terrifying side of Nazi Germany, the passionless and soulless bureaucrats in grey paramilitary attire organizing mass executions like they were organizing the supply of office stationery to the local welfare administration offices of a small province. But overall Fascist society would be more similar to Nazi Germany in a sense (though, it would definitely be less successful in terms of totalitarian penetration due to a stronger Church, historically lower efficiency of conversion, radicated Marxist resistance, and generally an higher tendency in Italians of just doing the fuck they want). This doesn't mean Italy and Germany will have to remain allies and the evergreen trope of Italy being the China to Germany's USSR and changing sides has to be shelved, just that tensions will happen due to conflicting interests, and any opening to the Allies would be an extremely utilitarian one like the visit of Nixon to China, with Italy's lower propension to exterminationism being enough for the hawks in DC and London to accept the compromise in the name of fucking over Germania. Fascism can still fall or maybe wither, it's just that it's not an automatism like other TLs assume.