In trying to figure out what term to use, three main terms come to mind: (1) "Tridentine Mass," (2) "Extraordinary Form (EF for short)," and (3) "Traditional Mass" or "Traditional Latin Mass (TLM)," and its variants. But I think the terms "Tridentine Mass" and "Extraordinary Form" are a bit unfortunate, for different reasons, which I will explain. I will also (4) address your comment that the novus ordo, too, is traditional, and (5) will make some concluding remarks.
(1) I think using the term "Tridentine Mass" is a disservice to the cause, in a way. One of the marvellous aspects of the ordo antiquus is its patristic origins: it connects us in a living way to our fathers in the faith, to the way they lived it. It was the Latin Church Fathers who bequeathed this amazing gift to us, and we see their stamp in the way we worship every Sunday in the ordo antiquus (or every day, in some parishes). But the "Tridentine Mass" terminology blurrs this reality and promotes the erroneous idea that the ordo antiquus can only be traced back to the liturgical reforms after the Council of Trent (16th century), and that before then the Roman Rite was substantially different, and that therefore the current rite that we know as the "Tridentine Mass" has relatively modern origins. If anything it would have to be called the "Gregorian Mass" to indicate that it is much older and can be traced at least as far back as St. Gregory the Great (6th cent.), just like we say "Gregorian Chant" to indicate the Latin Patristic origins of the music that belongs to that Rite. That terminology would also mirror our Byzantine brothers and sisters who have the Liturgy of St. Basil, the Liturgy of St. John Chrysostom, etc. I would in fact prefer the terminology of the "Gregorian Mass", but alas, it is not a very common or accepted terminology, and it is in fact already used to refer to something else (the 30 Gregorian Masses devotion).
And (b), the term 'EF' is too narrow, and not broad enough to encompass the other Latin rites. In fact, one of the churches that commonly has Massses that are of our interest is Holy Rosary Parish, in Portland, where the Dominicans there have several Dominican Rite Masses every month. These Masses are not technically in the EF, because that term applies exclusively to the Roman Rite, as per Summorum Pontificum. Rather, the Dominican Rite has no extraordinary form. The Dominican Rite has only an ordinary form which has remained substantially unchanged throughout its history and has not been touched by the recent liturgical reform. So if we were to announce only "EF Masses" we would be leaving out these Dominican Rite Masses, which are of interest to the TLM community in our area.
(3) So it is mainly because of these reservations (which I believe are shared by many TLM communities), I naturally lean towards using the term TLM as the normal way to refer to the ordo antiquus. But besides the fact that the other alternatives are not good choices, I think the primary reason for using this term is that in itself it is clear enough simply because it is the way most people have referred to it in actual practice, at least in my experience in the last 15 years attending the old rite in the USA, Canada, Mexico, and Europe. It is the term ordinarily given to the ordo antiquus by traditional Catholics. (And by 'traditional Catholics' I mean those of us who are attached in an exclusive way to the ordo antiquus and the mode of thinking surrounding it, and who are steeped in it enough to let it be the basis of their faith in an exclusive, or nearly exclusive way.) See for example the terminology used in websites such as Coalition in Support of Ecclesia Dei: Promoting the Traditional Latin Mass as sanctioned by Summorum Pontificum, and its widely-used Directory of Latin Masses, as well as the normal terminology in the popular blog "Rorate Caeli," and specifically its discussion on this very issue of the terminology of the ordo antiquus. It is the way it is called in the most widely-used Latin-English missalette (see picture above), and it is the way it is called by most members of the Priestly Fraternity of St. Peter, the Institute of Christ the King, and similar orders that are devoted to the ordo antiquus and who celebrate the vast majority of Masses in the ordo antiquus. So it is safe to say that I can hardly be blamed for doing the same. In fact, no one who regularly uses the information on the site---which is usually traditinal Catholics who are willing to travel throughout the Willamette Valley to attend one of these Masses---have so much as hinted to me that there might be a problem with the term. Although in conversation and in print I have become aware of many objections regarding the other terms.
(4) Now, I must confess I was a bit surprised by your comment that the novus ordo, too, is traditional (and not just the ordo antiquus). I think we must make distinctions here. In all philosophical objectivity, we have to recognize that the term 'traditional' is very much an analogical term. It obviously does not mean the same thing when I say that the ordo antiquus is 'traditional' as when you say the novus ordo is 'traditional'.
The ordo antiquus is traditional because it is the form of worship that Roman Catholics have been 'handing down' from generation to generation for close to two millenia. This is the way the vast majority of popes and saints in our calendar have worshipped. St. Jerome, St. Gregory, St. Leo, St. Isidore, St. Anselm, St. Bernard, St. Francis, St. Thomas, St. Catherine, St. Pius V, St. Ignatius, St. Frances, St. Joan of Arc, St. Teresa of Avila, St. Alphonsus, St. Margaret Mary, St. John Bosco, St. Therese, St. Pius X, St. Josemaria, just to mention a few, all worshipped according to the ordo antiquus (even if in the various Latin rites), and their faiths were formed exclusively by it. Hence, it is in the strong sense that the ordo antiquus can be called the TLM, since it refers to the Mass according to the tradition of the Latin Rites.
But the novus ordo is not 'traditional' in the sense that the ordo antiquus is traditional. It is quite discontinuous with the tradition of the Latin Rites; a careful comparison of the prayers (and options) illustrates this amply. So if for the sake of argument we grant that the novus ordo is 'traditional', to make that a true statement we would have to change the meaning of 'traditional'. But that meaning would definitely not be the normal use of the term, the sense in which most people use it.
To be clear, here I am simply making a descriptive claim, and not a normative one. I am simply observing that the novus ordo is a significant departure from what has been handed down to us from time immemorial. So it cannot be called 'traditional' in the sense in which the ordo antiquus is traditional. I'm not saying that "the present Order of the Mass is an abomination" or anything of the sort. And I actually admire you for your courage in saying the novus ordo in Latin in this diocese; may God reward you for that. But obviously, you would agree that if you were to celebrate a novus ordo Mass in Latin and called it the "Traditional Latin Mass," and advertized it as a TLM (without telling them you really mean the novus ordo), you would really be confusing them, because that is not what everyone understands by that term.
But ultimately, Father, I think you are right in saying that language matters, and in pointing out that the term "Traditional Latin Mass" is not perfect. I would agree that it is not totally unambiguous. And I would even grant that the particular variant "Latin Mass" is indeed very ambiguous. In fact, given these reflections, I might therefore change the name of the site from "Willamette Valley Latin Mass Society" to "Willamette Valley Traditional Mass Society," or something like it. I will pray about it.