I don't know much about Portuguese history but I don't see a problem in anything you state being contrary to fascist aims. I think the first question is to ask however what is fascism, and what is fascist thought? This is actually a question I have pondered many times before and have wondered about this question, but thankfully we have Mario Palmeri to provide us the answer. In his book The Philosophy of Fascism he states: "He who thinks of Fascism and its worth thinks, primarily and above all, of what Fascism stands for in the realm of the spirit; of its contribution to man’s spiritual heritage." In this very quote we see fascism as a spiritual philosophy, and Palmeri continues to enlighten the meaning of fascist thought in this quote:
"Fascism is an eminently idealistic and, more specifically, an anti-materialistic and anti-individualistic philosophy of life. These characteristics are clearly expressed by the recognition of the eternal value of the spiritual essence of man and of the transitory aspect of his earthly being; by the recognition of the absolute worth of the individual in the realm of the Spirit and of the relative worth of the individual in the realm of Nature; by the recognition of the transcendent significance of the historical process and of the fundamental continuity of human history; by the recognition of the supreme role played in the life of mankind by those social formations called Family and Nation, and of the small importance of the role played by the single individual; by the recognition of the influence of Religion on human life, and of the supremacy in this life of Ethics over Economics, of Art over Business, of Poetry over Science, of Intuition and Inspiration over Experience and Method; by the recognition of the supremely ethical nature of the State, and of the function of the State as concrete expression in the realm of time and space of the timeless idea of the nation; by the recognition of the truth that mankind needs an aristocracy of leaders led, in turn, by national heroes; of the need that the doctrine of the Rights of Man; of the fact that Man lives not by bread alone but also, and mainly, of beliefs; and, finally, of the truth that all forms of personal freedom pale in contrast to that form of Liberty which only has meaning and truly matters: the Liberty of the Spirit."
In that quote Palmeri states quite clearly that fascism rejects materialism and individualism, therefore the fact that what you stated about the Fifth Empire being inherently spiritual instead of material is exactly what fascism is, fascism rejects materialism. In your quote about mysticism, fascism too seeks to bring it about, Palmeri's quote:
"And, yet, there has never been a more forceful appeal made to the best in man than the appeal made by Christianity. The idealism born of it, and constituting in a way its main characteristic feature, spoke always directly to the Soul and through the Soul. It spoke of a world of values which were not of this earth and which far transcended everything which the earth could offer. It spoke of another life, more alluring than the present earthly one, a life unseen by mortal eyes, but, nevertheless, far more vivid than any other thing perceived. It spoke, finally, of the existence of another form of reality, unknown to man in his ordinary state, but of which he could get fleeting glimpses in his rare moments of mystic consciousness; and, speaking of this reality as the only reality, it denounced the one apprehended by the mind through the intermediary of the experience of the senses, as a most illusory and deceiving one."
Palmeri later stated that this was the message delivered by the religious idealism born of Christianity, and fascism seeks to bring about this type of idealism but a new type of idealism spoken by Palmeri: "Such must the distinguishing features of the new Idealism be; such indeed are the distinguishing features of Fascist Idealism."
Fascism uses myth and believes firmly that man is made of soul and spirit and is not made of material, to denote man to mere material is something fascists find vehement about and rejects it with passion.
Gentile in his book the Origins and Doctrine of Fascism states:
"The Italian Fascist state- for reasons already given- one with the mass of Italians, is either not religious or it is Roman Catholic. It cannot be irreligious, because the absolute value and authority it confers on itself would be incomprehensible without a relationship to the divine absolute."
In the quote above Fascism does not reject the divine instead it sees a relationship to the divine absolute as something that is necessary to fascism, so when you said: it is a divinely inspired leadership whose only purpose is to bring the Millennial Kingdom, I see no such conflict with fascism when fascism too also incorporates a relationship to the divine. It also incorporates mysticism and seeks to bring this about in a new idealism that calls to the men of today.
Hopefully you find this interesting

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Online source of Origin and Doctrine of Fascism by Gentile:
https://archive.org/details/OriginsAndDoctrineOfFascismGiovanniGentile/page/n41/mode/2up
Online source of The Philosophy of Fascism by Palmeri:
http://thephilosophyoffascism.blogspot.com/2014/07/the-philosophy-of-fascism-by-mario.html