The question concerns the lingua franca of the population of Palestine, not the language employed in writing the Torah.
If we are assuming that 'Jews' wrote the gospel (who else would write a Hebrew text) and the Torah gives 613 commandments, by what authority did the Jewish Christian converts undo their obligation to the Torah? The answer is of course, the Evangelium, and the gospel is the word of Jesus. The assumption regarding a Jewish underpinning to Christianity necessarily constrains how the gospel was understood.
Take the example of the money-changer saying in the middle of the dialogue with the priests (Mark 10, Mark 12) in the Hebrew gospel. Jesus says essentially there is a difference between what God said (the ten utterances) and what Moses said (the rest of the commandments). This POV is attested in the rabbinic writings as both 'Sadducean' and heretical (Christian). Heschel notes that when Jesus says effectively (a) God said X (b) Moses said Y but (c) I reaffirm X it confirms the rabbinic traditions understanding about Christianity. But Heschel didn't recognize that the reference to Genesis 1:27 in the Damascus Document also echoes Jesus POV in Mark 12. Heschel was an expert in the rabbinic tradition not the Qumran literature.
The point nevertheless is that it is correct to identify a 'Jewish origin' for Christianity but that when you do so you inevitably end up identifying the earliest Christians with the opponents of the rabbinic tradition who are otherwise identified as the 'two powers in heaven' tradition. The connection is not explicitly made in my knowledge in any material related to the Christian exegesis of Mark 10 or Mark 12 or the passages related to these texts in the Pentateuch. Nevertheless when we start asking ourselves the question that keeps popping up in the gospel - 'by what authority do you say these things' (a question which Jesus refuses to answer in our texts) we start to edge towards a solution.
By what authority did Christians abandon the law of circumcision? It is never spelled out in any logic form in the surviving canon but the answer is clearly linked to the 'money-changers' saying or what Heschel calls the concept of a 'heavenly Torah.' When Jesus says:
(a) God said X (b) and Moses said Y but (c) I reaffirm X
One can see him as a reformer, a conservative or whatever other label we want to give him but the authority to ignore Moses cannot be taken lightly. If the argument was made that God said one thing, Moses said another and we only accept what was 'god-given' (= the idea behind the name Dositheus, a prominent Samaritan heresy) the 'money-changer' - i.e. Jesus - had to have a greater authority than Moses. He doesn't necessarily have to be the angel who gave the ten utterances to Moses (I say this just to avoid getting dragged down to an unnecessary debate), but clearly this what the early Christians believed (i.e. Justin, Clement, Irenaeus etc).
In other words, we can develop a complicated scenario where Jesus was a man who was held to be greater than Moses and that this is why Christians had the authority to pick and choose which commandments they deemed God-given, but the straightforward answer is to follow the Church Fathers again and identify Jesus with the angel who gave the ten utterances to Moses. As such the gospel is the second Torah and this explains why the text was understood to have been written in Hebrew, rather than Aramaic.
I know this is not going to make sense to avi, but I hope it makes sense to someone else that might be reading this. The bottom line is that the 'Jewish origins' for Christianity is a Pandora's box for those hoping to buttress the neo-Protestant assumptions about a 'historical Jesus.'
