Well only Jews were allowed in the synagogue, so Acts 19 should not be referring to Gentiles. As for Acts 28, again you are arguing from silence that those are non Jews. Scripture did not say.
But even if I grant you that point, that there were Gentiles, the real difference between the GOK preached by Paul and the one preached by Peter in Acts was that, at no point, Paul offered the physical return of Jesus to his listeners if they accepted Jesus as their promised Messiah, unlike what Peter did in Acts 3:19-20.
So no, Paul did not preach the same GOK as Peter did.
Paul says in 1 Timothy 6:3-4, if any man does not agree with the words of Jesus Christ and the doctrine according to godliness, he is proud and he knows nothing.
James 4:6 says God resists the proud and gives grace to the humble.
So if Paul believed Jesus taught something different in the sense that he did not agree with the words of Jesus Christ, and the doctrine according to godliness that came beforehand, Paul would be disqualifying himself by his own words here and he would be proud (whereby God would resist Him and not give him grace according to James 4:6).
Furthermore, Jesus said in John 12:48 that if any man receives not His words, those words will judge them on the last day (i.e. the Judgment). It is illogical to assume that Jesus only meant those words in John 12:48 as being during His Earthly ministry (pre-cross) only. It does not make sense for Jesus to give us new teachings, just so that they can be radically changed so quickly with His crucifiction (i.e. the official beginning of the New Covenant). Even Revelation teaches the necessity of obedience as a part of salvation.
Revelation 22:14 KJV says,
"Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city."
So you cannot escape doing good or living holy as a part of God's saving grace and salvation. The two go together like bacon and eggs. Grace and Sanctification both play a part in our salvation.
"...God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth" (2 Thessalonians 2:13).
2 Thessalonians 2:13 above here says that God has chosen us to salvation through:
#1. Belief of the Truth (i.e. Jesus is the Truth - John 14:6).
#2. Sanctification of the Spirit (i.e. Holy Living - 1 Thessalonians 4:3).
For Romans 8:13 says if we live after the flesh (sin), we will die (die spiritually), but if we mortify (put to death) the deeds of the body (sin) via the Holy Spirit, we will live (live spiritually, i.e. eternal life).
So Paul is saying here that if we live one way, we are going to die, but if we live another way, we are going to live. Paul is speaking in spiritual terms.