In my studies on Early Church history, I would confirm most of your suspicions describing the broad use of Latin, Greek, and Aramaic/Syriac as the major liturgical languages of Christianity. But one important issue, is the importance of dialects. Many world-wide languages start out as a dialect of a major tongue only to grow and develop into eventually being considering being a language in their own right, and the same is true of Holy Languages.
Arabic Early Arabia had many Christians and Jews living there, many of which came as part of the Diaspora when Rome destroying Israel during "the Jewish Wars". These people were predominately Aramaic speakers. Besides that Arabia had been conquered in the Old Testament times by Assyria or Babylon, where the foreign invaders established Aramaic as its native tongue. In time, however the dialect grew and developed and became what we know as "Arabic". Depending where you are on the time line of Church History, you might count the Liturgical language of Early Arabs as being Aramaic or Arabic (500 AD).
Coptic As an official member of the Church of Alexandria, I can confirm that Coptic also suffers from some of the same category confusion, but does so with koine Greek. In many ways it can be just a dialect of Koine, many things written in Coptic seem identical word for word, and letter for letter. But there are some fine differences, there were two additional letters created for Coptic that go beyond the Koine alphabet (The were borrowed from by an Eastern Orthodox saint, and used for creating the Russian alphabet). But more importantly, certain ancient Egyptian words and phrases were retained. Here’s an example from the “Prayer of Hours”, Agpeya.
Ke nin ke a ee ke ees toos e onas toan e oa noan ameen.
“Now and forever and unto the ages of all ages, Amen.”
But probably the biggest reason why Coptic might be considered its own language is because some Early Church writings were written using the older hieroglyphic alphabet, and the hieroglyphic alphabet is still often taught, alongside the Greek Alphabet if you want to learn Coptic as a Holy Language.
Armenian is an interesting case. The Armenians were evangelized in New Testament times by Bartholomew and Thaddeus. But they did not have a written language until 405 AD when saint Mesrob invented their alphabet. He then began to translate the Bible into their new language (425 AD) and did the same for their liturgy.
I actually attended an Armenian (Oriental Orthodox) church for almost a year and heard a sermon on their history etc. The priest related that during the transitional time, the Church used Armenian as worship language in church, but when reading from the scriptures, creeds etc. they actually had to use Bibles and other books that were written in Greek or Syriac! So anyway, Armenian would not really be a full liturgical language until 0425 or so.
asserts that Christianity was introduced by the Eunuch who was the Finance Minister of Queen Candace in the beginning of the first century (34 A.D.), the Eunuch being baptized by St. Philip the Apostle. (Acts 8:26-39) He preached the Gospel around the palace in Aksum but the sacrament of Eucharist and Baptism were not performed until the arrival of Frumentius, the first Bishop of Ethiopia.
The Book of the Contending of St. Tekle Haimanot3 tells us that Frumentius (Sidrakos) and Adesius 4 came from Jerusalem to Ethiopia in the beginning of the fourth century A.D. They were received by the High Priest Anbarom where they grew up learning the life and customs of the country. One day Frumentius expressed how he himself was impressed by the devotional lives of the people towards their God. He then said to Anbarom, ‘My Lord, I admire the life and culture of the people, but you Ethiopians practice neither baptism nor receive communion.” Anbarom replied, “Our Fathers the Levities brought us circumcision and the Finance Minister of Queen Candace (Eunuch) brought us the faith of Christ, yet we do not have an Apostle who can administer the rite of Baptism and the Eucharist, so would you please go to Alexandria.” This he did. Then Patriarch Athanasius consecrated him Bishop and sent him back to Ethiopia. (A.D. 329—356) He was called Abba Selama (Father of Peace). He then administered the sacraments to the people. The High Priest himself, who was after the order of Judaic tradition, was first baptized and ordained Priest. Since then Eucharist and Baptismal sacraments were in practice throughout most of the country.
There is no clear information on which Liturgy or Anaphora Frumentius had brought with him from Egypt. The Ethiopian Synaxarium states that he translated the Old and New Testaments and other texts from Hebrew, Latin and Arabic into Geez. The Synaxarium continues to say that his work of translation was not completed. It was rather left for the Syrian Monks (Nine Saints) who arrived at Aksum in the 5th century. They are generally audited for the work of translation of the Scriptures and other literature from Greek, Hebrew, Syriac and other languages into Geez, and in propagating the Gospel and setting up the monastic order and schools. There is no clear information concerning the Liturgical work either by Frumentius or by the Nine Monks. Nevertheless the complete work of translation must be attributed to the Nine Monks with respect to the effort made by Bishop Frumentius since the Eucharistic worship was in practice and since the existence of the Liturgy is understood during his time.
The Liturgy of the Ethiopian Orthodox Tewahedo Church
Besides this I thought there existed some possibility of an Indian Christian Holy language (since saint Thomas is said to have evangelized India around AD 52). But I can't find any hard evidence. There definitely was a Christian presence from early Aramaic Christians living on the spice and silk trail, and later from Missionary Activity from the Eastern Syriac Church. But it seems like it wasn't until the middle ages where Malayalam was used as a liturgical language.