How about an earlier, and more populous Germanic migration to the south in the 1st Century BC, so that during the height of the Roman Empire there is a loyal Gothic Kingdom in the Carpathians. When Judaea starts revolting, the Empire decides that instead of dispersing the Jews, inserting loyal Roman citizens into the province would be a better way to keep order, among the people encouraged to migrate to Judaea are a fair few Germans, this sets about a subtle linguistic revolution in the Jewish homelands.
Eventually, the Empire is split into the North-Western Roman Empire, and the South-Eastern Roman Empire, with the latter's capital based in Alexandria.
Some time after that another grand migration of Germans takes place, this time, the Vandals. Instead of heading into Hispania, which has been kept secure by North-West Rome, instead they travel across the relatively unprotected Bosphorous and eventually settle in the Syria and Judaea. Although in this world Arianus has been butterflied away, the Vandals still follow a dangerously unorthodox version of Christianity. Alexandria views the Vandals in Judaea as a threat, and struggles to keep them under wraps.
By about the 9th Century, the constant Turkish invasions to the north of Alexandria eventually cause the Empire to give up its Asian territories, and concentrate instead on North Africa. Without their mutual Alexandrian enemy, there is a power struggle between the Jewish and Vandalic leaders, which often resorts to all out war. However, as both sides appear to be evenly matched, the appetite for conflict is soon lost after a century or so. And after that, the two communities generally coexist peacefully. Their new land begins to be known as Juhdlond, and their language as Juhdische (close enough, eh?). The tongue is shared by Jew and Vandal alike, and is much like OTL Yiddish, but with a bit more Hebrew and a lot more Greek influence.
Although, no formal constitution is ever considered, a lot of conventions gradually make it into law. Firstly, all inhabitants of Juhdlond (who have inhabited Juhdlond since the ATL 'hetrarchy', are to be considered Jews, however, this concentrates more on Jewishness as a national identity, and not as a religion, as such, there is no contradiction between being a Jew, and being a Christian of any sect (that does not owe allegiance to Rome or Alexandria). The head of state is the 'Koenig von der Juhden', and below him is a culturally Germanic feudal system.
In TTL, Islam is butterflied away, and thus Juhdland has a much easier time expanding eastward, and manages to secure a significant Arab slave population. Without Islamic influence, the Persian Empire converts to Christianity, of a cohabitationary form more closely ressembling that of Juhdlond's Christians than that of either of the Romes. Juhdland and Persia remain friends for most of their history.
As Alexandria's North African bread basket desertifies, and Rome's provinces become increasingly ladden with disloyal immigrants, both Empires begin to decline, and Juhdland fills that gap. The Juhdische Kaisarreich expands south down to Yemen, and north into Anatolia and the Ionian shores. The Kaisarreich's jovial relations with Persia make it an essential player in the trans-Eurasian trade network. This, combined with Juhdlond's much more liberal approach to usury quickly make it a very rich nation, and by the 14th Century, Juhdische has replaced Latin and Greek as the linguae franci of the Mediterranean.