Hmm, you seemed to miss something very big from the bible. At the end of Acts 21 there was a crowd that wanted to kill Paul but he was saved by Roman soldiers. He asked the captain to allow him to speak to the people. The bible said, "And when there was made a great silence, he spake unto them in the Hebrew tongue, saying, Men, brethren, and fathers, hear ye my defence which I make now unto you. (And when they heard that he spake in the Hebrew tongue to them, they kept the more silence: and he saith,)" He goes on to make his defence to them, explaining how he persecuted the Christians until Christ came to him on the road to Damascus. He stated that Christ said unto him, "Depart: for I will send thee far hence to the Gentiles." Luke then records, "and they gave him audience unto this word, and then lifted up their voices, and said, Away with such a fellow from the earth: for it is not fit that he should live."
Ok, so we have Paul speaking to them in Hebrew. Apparently Hebrew wasn't quite as lost as you thought. When he spake to them in Hebrew, they kept the more silence. Why? Well, it was their tongue. The Gentiles that were there couldn't understand what he was telling them. Finally, when he tells that Christ said He would send him to the Gentiles, Luke said they gave him audience until that word, and then they cried out for him to be killed. The fact is, these Jews hated the Gentiles. They didn't like the Romans being there, they thought the Gentiles were dogs, and they especially hated the idea of the religion going out to the Gentiles. The idea of a religious message being given on an equal footing to Gentiles, and Gentiles being equal with Jews in religion was offensive to them.
Given all these facts, I find it hard to believe that Jesus preached from the LXX. Is it possible? Yes, I wasn't there. But it just doesn't add up to Jewish notions at the time.
Paul, though probably possessing actual Hebrew skills as trained by one of Israel's finest teachers, spoke not in Hebrew, but in the dialect of the Hebrews, in other words, Aramaic. Virtually every commentator agrees. Hebrew was not a common spoken language at this time.
Here is one of the places where insistence on a KJV translation has let you down and suggested something that is not precisely translated. The Greek says "hebrais dialektos" = Hebrew dialect, not Hebrew "tongue," which would imply, as you suggested, that the actual language of Hebrew was spoken by Paul.
Jamieson-Fausset-Brown Bible Commentary:
"in the Hebrew tongue-the Syro-Chaldaic, the vernacular tongue of the Palestine Jews since the captivity"
Wesley's Notes:
"In the Hebrew tongue - That dialect of it, which was then commonly spoken at Jerusalem (Aramaic)"
Vincent's Word Studies:
"Lit., dialect: the language spoken by the Palestinian Jews - a mixture of Syriac and Chaldaic"
Gill's Exposition of the Entire Bible:
"he spake unto them in the Hebrew tongue; which the people he spoke to best understood, and was his own mother tongue; the Alexandrian copy reads, "in his own dialect"; this was not pure Hebrew that was spoke in common in those times, but the Syro-Chaldean language"
Clarke's Commentary on the Bible:
"He spake unto them in the Hebrew tongue - What was called then the Hebrew, viz. the Chaldaeo-Syriac; very well expressed by the Codex Bezae, τῃ ιδιᾳ διαλεκτῳ, in their own dialect."
Barnes' Notes on the Bible:
"In the Hebrew tongue - The language which was spoken by the Jews, which was then a mixture of the Chaldee and Syriac, called Syro-Chaldaic. This language he doubtless used on this occasion in preference to the Greek, because it was understood better by the multitude, and would tend to conciliate them if they heard him address them in their own tongue."
About "Jewish notions at that time..." I humbly suggest a study of Jewish culture. They were very Hellenized. Greek or Aramaic were the languages of the day.