Ben, you are the first person I have ever run across who says that Unam Sanctum is considered to be an infallible teaching. What is your source for that statement?
It has been defined three times that only those who die as Catholics can be saved:
Pope Innocent III, A.D. 1198-1216: Ex cathedra: "One indeed is the universal Church of the faithful, outside which no one at all is saved." (IV Lateran Council, A.D. 1215)
Pope Boniface VIII, A.D. 1294-1303: Ex cathedra: "We declare, say, define, and pronounce that it is wholly necessary for the salvation of every human creature to be subject to the Roman Pontiff. The Lateran, November 14th, in our eighth year. As a perpetual memorial of this matter." (Unam Sanctam, A.D. 1302)
Pope Eugene IV, A.D. 1431-1447: Ex cathedra: "It [the Holy, Catholic, and Apostolic Church] firmly believes, professes, and proclaims that none of those outside the Catholic Church, not only pagans, but neither Jews, or heretics and schismatics, can become participants in eternal life, but will depart "into everlasting fire which was prepared for the devil and his angels" [Matt. 25:41], unless before the end of life they have been added to the Church; and that the unity of the ecclesiastical body is so strong that only to those abiding in it are the sacraments of the Church of benefit for salvation, and do fastings, almsgiving, and other functions of piety and exercises of Christian service produce eternal reward, and that no one, whatever almsgiving he has practised, even if he has shed his blood for the name of Christ, can be saved, unless he has abided in the bosom and unity of the Catholic Church." (Council of Florence, A.D. 1442)
Two of these definitions, are from Holy and Venerable Ecumenical Councils. The Church has always held that all of the ecumenical councils are ex cathedra, infallible; (Vatican II is an exception as the Pope chose that it be only a pastoral Council; Paul VI stated that he did not promulgated it as ex cathedra; that is however the only exception to the rule.)
We can see this from the ex cathedra teaching of Vatican I. When papal infallibility was defined, the Council said the following:
"Therefore, faithfully adhering to the tradition received from the beginning of the Christian faith, to the glory of God our saviour, for the exaltation of the Catholic religion and for the salvation of the Christian people, with the approval of the sacred council, we teach and define as a divinely revealed dogma that when the Roman pontiff speaks EX CATHEDRA, THAT IS, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, HE DEFINES a doctrine concerning faith or morals TO BE HELD by the whole Church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his Church to enjoy in defining doctrine concerning faith or morals. Therefore, such definitions of the Roman pontiff are of themselves, and not by the consent of the Church, irreformable. So then, should anyone, which God forbid, have the temerity to reject this definition of ours: let him be anathema." (Denz. 1839)
So, when a pope "defines" something "to be held" it is "ex cathedra". But, in the run up to this, the Vatican I also defined:
"Moreover, the Roman Pontiffs, according to the dictates of time and circumstances, sometimes by calling ECUMENICAL COUNCILS or asking the opinion of the Church dispersed throughout the world, sometimes through particular synods, sometimes by using other means which divine providence supplied, DEFINED those things which MUST BE HELD and which they knew, by the help of God, to be consonant with the Sacred Scriptures and apostolic traditions." (Denz. 1836).
So, prior to Vatican I, popes "defined", things which "must be held" - and called ecumenical councils to prepare for this. But, as we just saw, when he does that, it is ex cathedra. Therefore, we may see from the teaching of Vatican I that there have been many ex cathedra definitions prior to Vatican I - particularly those which came upon the invocation of ecumenical councils.
From Unam Sanctam:
"Indeed we declare, say, pronounce, and define that it is altogether necessary to salvation for every human creature to be subject to the Roman Pontiff"
It is clear Pope Boniface was meeting the requirements of speaking "ex cathedra".
I am surprised you haven't heard this before, I haven't even met a NO priest who denies Unam Sanctam to be infallible.