There is no Aramaic Tanakh - you mean Aramaic Targums, which are a Judeo-Aramaic translation of the Hebrew Tanakh (Old Testament) which predates the Latin Vulgate translations from the Greek, Hebrew and Aramaic (as well as the Old Latin - which was direct from Greek LXX.) The notable issue with the Aramaic Targums (as with the Syriac traditions with the New Testament texts) is the free reign given to the 'translators' who combined, simplified, and often paraphrased rather than a literal translation. The Aramaic Targums, however, post-date the LXX (and of course, the postulated 'Old Greek' text). For that matter - our oldest Hebrew or Aramaic OT texts are newer than our oldest Greek texts (the Qumran/Dead Sea scrolls material points to a Hebrew tradition as well that bolsters the Greek translation, as well as texts that agree with neither the LXX nor the Masoretic/Targum tradition.) The Peshitta Old Testament texts are considered the *last* of the Old Testament texts to derive from the Hebrew (far younger than the Greek, and younger even than the Latin.)
For New Testament: the Khaburis Codex is not complete as it is missing 5 books found in the Western Syriac Peshitto. We have contemporary records from China that describe the list of books in the East Syriac Peshitta some three hundred years previous as having the full canon. Carbon dating has placed the Khaburis Codex at only about 1000 AD. However, the oldest New Testament fragments we have date to 125 AD, and are the Gospel of St. John in Greek (papyri from Egypt.) The dating of the vagantes mentioned in the article is a bit off. The Aramaic and Syriac texts *do* bear translated quotes from the LXX recension of the Old Testament, as well as Semitic approximations of Greek names born by the Apostles and other Disciples of Christ. We have Greek texts for every text of the New Testament by the year 300, many of them with older examples from Egyptian papyri (the Pauline Epistles no younger than 200 AD.) So, the claim for an East Syrian text as the oldest has little more than an appeal to authority by the Assyrian Church of the East (the same one's who claim Nestorius didn't influence them, though they pray a good part of the year with his anaphora.) I believe that there is only solid theory behind a Semitic language original for the Gospel of Matthew, and possibly the Epistle to the Hebrews (the latter most scholars don't agree with, and that the letter was composed to the majority Greek speaking Jews.)
As for the 'Aramaic puns' - what is read in this case is present in the Greek, as the Greek is rather a Judeo-Hellenic Greek - the Semitic turn of phrase is in the oral language, preserved literally in the new language (Greek), and recovered when paraphrased back into a Semitic language. Others (such as the gamal/gamla argument) aren't enough to base a theory of a complete 'pure Semitic' text for the whole New Testament. However, the political influence of the Persian Empire to be anti-Western (anti-Roman, anti-Greek, etc.) does offer an explanation as to the imperfect attempts to purge the East Syrian consciousness of the multi-lingual "border" quality of the 1st century Christians in Palestine - a situation which the Church in Jerusalem and environs retained through the days of the pilgrim Egeria, and possibly even after Theodore Balsamon. (How much modern anti-Establishment philosophy plays into this as well - being anti-Indo-European language is a sort of radical embracing of the 'common man', Marxist principles, "Black theology" and identification of Latin, Coptic, Greek and West Syriac as 'oppressor languages' and East Syriac as the 'oppressed language' - which probably explains the fascination with East Syriac Peshitta and Nestorian theology for post-hippie Middle Class Westerners.)
Greek, of course, is the 'other language' that Christ and his Apostles spoke. Only Judas Iscariot (being the lone Judaean) had the possibility of being a monolingual Aramaic speaker. Galilee, however, was a bastion of Hellenic speaking Judaism. Monolingual Jesus (and Apostles) is simply a bad theory (for that matter, we can be pretty sure Jesus also spoke Coptic besides Aramaic and Greek... and possibly even proto-Arabic and other languages.)
