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SSPX preserves the Catholic faith as it was believed and practiced before the Council and before the New Mass came into vogue, both of which gave modernism the illegitimate means whereby to wreck the Faith.

“We think, how grievously they err who arbitrarily claim that the Church is something hidden and invisible, as they also do who look upon her as a mere human institution possessing a certain disciplinary code and external ritual, but lacking power to communicate supernatural life” (par. 64)

But we must not think that He rules only in a hidden or extraordinary manner. On the contrary, our Redeemer also governs His Mystical Body in a visible and normal way through His Vicar on earth. . . . Since He was all-wise He could not leave the body of the Church He had founded as a human society without a visible head. . . . That Christ and His Vicar constitute one only Head is the solemn teaching of Our predecessor of immortal memory Boniface VIII in the Apostolic Letter Unam Sanctam; and his successors have never ceased to repeat the same (par. 40).
..... Pope Pius XII’s encyclical Mystici Corporis

Can a Catholic be faithful to Traditional Rome, without remaining faithful to temporal Rome?

According to Pope Pius XII ..... No!

"Can a Catholic be faithful to Traditional Rome, without remaining faithful to temporal Rome? According to Pope Pius XII ..... No!"

But there was the assumption, made here by Pius XII, that the papacy supports Tradition as any pope is obliged to do. If the pope does not, if he supports novelty instead, then the faithful are forced to choose between the pope and the faith, between the novel teachings of this pope and the teachings of the preconciliar popes, including Pius XII himself.

In any case, SSPX does not deny the Pope is the head of the Church as you seem to suggest. This is why it prays for the Pope at all Masses and officially affirms his role as head of the Church. But it refuses to deny the faith by following the New Order he wishes to impose. The Faith after all is the reason for the papacy's very existence. Above all else the pope is pledged to protect the deposit of faith. If he does not do this, then we must place the faith first, even before the pope.