In a way it doesn't matter since epistles predate Luke and talk about the main points in the Gospel anyway.
I suggest you start actually reading the epistles. There is practically nothing in them that confirms much of the gospels, except that Paul says that Jesus instituted the Eucharist, that the crucifixion occurred, and that some sort of resurrection occurred - but a spiritual one only. Nothing of the nature of the completely contradictory details in the gospels.
Furthermore, he effectively wipes out just about all the Jewish law, in order to instate his own peculiar theology. If you accept that Jesus said 'not one jot nor tittle of the Law shall pass away', you can't avoid these well known facts (given full attention for over 200 years, and in particular by Schweitzer)
That there are sentiments in Paul's writing that Jesus might well have admired (such as the famous chapter on 'Charity') does nothing to confirm your erroneous suggestion that the Epistles support the gospels in essentials.
They don't. Much of those details owe more to the writers' imaginations or the assemblage of stories long in circulation, which may well have originated with other preachers other than Jesus in any case.