If it is true that the 4 Gospels existed in Aramaic by at least 78 AD, what evidence is there for the rest of the New Testament?
Start with what Peter says. In II Peter, he references Paul's multiple letters having been available and read by those Peter is addressing.
[2Pe 3:15-16 LSB] 15 just as also our beloved brother Paul, according to the wisdom given him, wrote to you, 16 as also in all [his] letters, speaking in them of these things, in which are some things hard to understand, which the untaught and unstable distort, as [they do] also the rest of the Scriptures, to their own destruction.
Peter's audience had been able to read what Paul had written. So who was Peter's audience. We find out a few verses previous:
[2Pe 3:1 LSB] 1 This is now, beloved, the second letter I am writing to you ...
Who was the first letter addressed to?
[1Pe 1:1 LSB] 1 Peter, an apostle of Jesus Christ, To those who reside as exiles, scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia, who are chosen
It was to the Christians of Jewish heritage who were living outside of the Jewish homeland. Where are those places? In modern day Turkey. So the writings of both Peter and Paul had made it through that entire area. They were able to read it in a language they understood. That language was Aramaic and not Greek. Aramaic was the lingua franca outside of the Roman Empire. It was the lingua franca of the Jewish people whether in their homeland or those living in exile. This is demonstrated in Acts 21:26-40. Paul is arrested after some visiting unbelieving Jews slander him and rile up the residents of Jerusalem. The Roman commander arrests him and is just about to put him in prison. Paul talks to the commander in a different language and he is shocked to hear Paul speaking Greek. This convinces the commander that Paul is being slandered and Paul is allowed to address his accusers - in their own language. He does not speak to them in Greek but in their own language - stated to be the language of the Hebrews.
So things are not as we have always been told. While Paul did know Greek, that does not mean the entire Jewish population knew or spoke Greek. And the content of the New Testament probably was not originally in Greek. But it was translated very soon after being written in Aramaic.