I think for many purposes, Orthodox have to say the document is suspicious because of its explicit agreement with what Rome claims about herself. However many historical documents we have today are reliable even without the original (cough cough, the Gospels) yet they are fully trusted.
Apples to Oranges. The Gospels are trusted because the Church determined through their catholicity and orthodoxy (that is, through their agreement with the orthodox doctrine of Christ, and their use in many places throughout the Church) that they are trustworthy. The Gospels are not trustworthy based upon who the writer claims to be (for there exist many heretical gospels which claim to have been written by an apostle) or based upon whether an original document exists.
The supposed Letter of Maximus to Peter, however underwent no such process, as it is neither catholic as having been preserved and read as a source of doctrine in many churches of God, nor has it ever been approved by synods as orthodox in its faith. And you are incorrect to say that we say it is suspicious because it resembles what Rome says about herself. We are suspicious because the document does not exist in the language in which St. Maximus the Confessor wrote, Greek, and because the document makes suspiciously anachronistic claims about the Roman Church, claims which would not be made for several centuries after the Confessor’s Death. Furthermore, as I pointed out, it makes an elementary error in claiming that the canons granted Rome a supreme and universal Jurisdiction, something which no canon from the first millennium does (a mistake that I am not inclined to think that St. Maximus the Confessor would make, but which many Latin canonists of the Second Millennium would make). Furthermore, we know that there are already several famous forgeries which were historically used to bolster papal supremacy, the Donation of Constantine and the False Decretals of Pseudo-Isidore being a large collection of such forgeries and interpolations. Why then should we give this document the benefit of the doubt when it does not exist in the language in which St. Maximus wrote, when it makes anachronistic claims about the see of Rome, and on account of the prevalence of forged and interpolated documents from this time period which bolster papal claims to power?
It would make logical sense that if the document were a forgery, there would have been at least one condemnation of it existing today from the time as it was circulated around the Church after his death. Yet there is silence as if there is approval and no contention as to the content of the Letter to Peter.
The argument from silence alone is not compelling. That the document only exists in translated fragments seems to indicate that it was not widely distributed. You would first have to prove that the document was widely disseminated and read for your argument to work
Secondly in Maxmus’s interrogation by Eastern prelates, we see his opinion towards Rome consistent with `what is in his letter to Peter. This even irritates the prelates to a point where they ask him :
Indeed, see how he says that he loves the Romans because they have one faith with him (which is to say that he is in agreement with their faith, and they are in agreement with his, not by any sort of compulsion, but by a true love for and faith in Christ), not because the See of Rome is the infallible see with which one must be in agreement on all matters of doctrine. This is no evidence for the case which you are trying to argue, namely, that the Roman Pontiff is infallible on matters of faith and morals, and that it is necessary to be in communion with him.
With regard to Pope Honorius, Maximus defends and proves that Honorius was not a heretic :
But this put you in a quandary. Who are you to believe, St. Maximus or Pope Leo II who wrote in his letter to the bishops in Spain exhorting them to accept the decisions of the Sixth Ecumenical Council that Pope Honorius would suffer eternal torment for teaching heresy? That Pope Honorius was a heretic, at least materially is undeniable, as an Ecumenical Council declared so, and anathematized him and ordered his letters to Sergius burned. You present one father who argued (partially for the reason that his allies at the time were from the Roman see, and to admit that a Roman bishop had taught monothelitism would be for him to concede defeat) that Honorius was not a heretic. We on the other hand have the witness of the Sixth Ecumenical Council, the Synod in Constantinople of 869-870 (which your Church calls the “Eight Ecumenical Council,” even though it was annulled by the later Council of Constantinople in 879) and numerous popes, all who affirmed that Honorius was an heretic. Who are we then to believe, one father (who was still fallible, despite the absolute steadfastness of his Christological and Cosmological doctrines), or the Catholic and universal witness of so many fathers and councils that Honorius was an heretic?