CathInfo.com

In their article they state that due to the duration of time that has elapsed since the promulgation of the new rite, if the new rite were invalid per se then we would have been left without a Catholic hierarchy which would be a violation of Our Lord's promise "the gates of hell shall not prevail against it" (Mt 16:18 )

Is that the only objection to admitting the invalidity of the new rite?  I ask because the term "Catholic hierarchy" is ambiguous.  You can distinguish between the ecclesiastical hierarchy which includes all men in the clerical state (i.e. who received first tonsure) and the jurisdictional hierarchy which includes only the clergy who possess an office which has ordinary jurisdiction attached to it.  i.e. the ordinaries.  Many traditionalists (clergy and laity alike) have an unsupportable opinion that the "gates of hell" will have prevailed if there isn't at least one ordinary in existence at all times.  However, you will not be able to find any pre-Vatican II Catholic theology manual which makes that specific claim.  It is a new claim which only came into vogue after Vatican II.  On the contrary both Msgr Joseph Clifford Fenton and Msgr Van Noort both implied that it was possible for the ordinaries to be wiped out.  Van Noort went so far as to say that the entire Catholic Church could conceivably be reduced to only the Pope and the few surviving clergy and laity of the Roman See.  Presumably, there would have to be at least one surviving bishop at all times because otherwise the Church would be lacking the means to accomplish her mission.  But as soon as a new pope is elected, he receives ordinary and universal jurisdiction directly from Our Lord.  So there is no need for an ordinary to exist at all times.  Also, Fr. O'Reilly warned that we should never put limitations on the depths to which Our Lord could plunge the Church.  Who would have believed that God could be crucified?

The old rites were formulated in such a way that if the minister followed the rubrics, their matter/form/intention was guaranteed, thus the validity was guaranteed.

The new rites' intention is no longer SPECIFICALLY part of the rubrics, therefore the validity is dependent upon the PERSONAL intention of the minister, which is a novel and dangerous situation, because no one can be 100% sure of the intention of anyone else.

Cardinal Ottaviani explains this dangerous situation in regards to the validity of the novus ordo's consecration, where he says that it may be "positively doubted" that the new consecration formula is valid because the intention of the Church is no longer specifically present in the canon and MUST be supplied by the minister alone.

The doubt about intention is an interesting topic but the new rites are already off the rails even before you get to the intention of the priest/bishop.  They changed the meanings of the rites so they have already introduced a doubt about validity even before considering the intention.  Even if you make the claim that it is only ambiguous and not clearly a new meaning, we are already in trouble because the ambiguity casts doubt on the meaning of the ceremony.  But I don't think there is any ambiguity at all.  The Novus Ordo clergy are very clear about the change in meaning by their words and actions.  Pope Leo XIII never bothered to investigate the intentions of the Anglican clergy.  He determined that the ceremonies themselves were sufficient evidence of invalidity.  And arguably the Anglican rites are closer to the traditional Catholic rites than the Novus Ordo sects rites.

Actually, I think this may be a critical question since the new rite of episcopal consecration is somewhat of a misnomer. It's not new. It's from the 3rd century Apostolic Tradition of Hippolytus.
It has been used and is currently used by the valid unbroken apostolic line of succession found in the Coptic and Western Syrian Rites (Maronite).
As the SSPX article states, "The Church does not judge about the mind and intention in so far as it is something by its nature internal; but in so far as it is manifested externally she is bound to judge concerning it".
I think the SSPX article sufficiently demonstrates that the new rite has valid form and matter...the question comes down to intention.
If the intention is not the intention of the Church, then the Coptic and Western Syrian Rite's have a problem (which as I understand it, has never been held by the Church).
So the earlier question cannot be just brushed aside. It's important to all of us in the Latin Rite seeking the truth re the validity of the new rite of episcopal consecration. It is not just an issue concerning the Eastern Rites.
In fact, it's possible to say this whole thread may now hinge on this question. I tend to favor Pax Vobis' initial line of reasoning, however, it is potentially running into a major problem here. Because if the Coptic and Western Syrian Rite's have a valid intention, and if intention is judged externally, then the SSPX position (on this particular topic notwithstanding other topics) may be correct after all.

Are we talking about the 2005 Angelus article?  Because in that article it is pointed out that the new rite is based on faulty research by Dom Bott.  He thought it was a consecration rite but it is actually an installation ceremony.  It is not the same as the Coptic rite.  And even if it was, it does not meet the minimal requirements for validity specified by Pope Pius XII.  You can read that in the 2005 article as well.