In his Commentary on John (10.2), Origen says this about harmonizations of discrepancies between the Gospels:
“The truth of these matters must lie in that which is seen by the mind. If the discrepancy between the Gospels is not solved, we must give up our trust in the Gospels, as being true and written by a divine spirit, or as records worthy of credence, for both these characters are held to belong to these works. Those who accept the four Gospels, and who do not consider that their apparent discrepancy is to be solved anagogically (by mystical interpretation), will have to clear up the difficulty, raised above, about the forty days of the temptation, a period for which no room can be found in any way in John’s narrative; and they will also have to tell us when it was that the Lord came to Capernaum. If it was after the six days of the period of His baptism, the sixth being that of the marriage at Cans of Galilee, then it is clear that the temptation never took place, and that He never was at Nazara, and that John was not yet delivered up. Now, after Capernaum, where He abode not many days, the passover of the Jews was at hand, and He went up to Jerusalem, where He cast the sheep and oxen out of the temple, and poured out the small change of the bankers. In Jerusalem, too, it appears that Nicodemus, the ruler and Pharisee, first came to Him by night, and heard what we may read in the Gospel. “After these things, Jesus came, and His disciples, into the land of Judaea, and there He tarried with them and baptized, at the same time at which John also was baptizing in AEnon near Salim, because there were many waters there, and they came and were baptized; for John was not yet cast into prison.” On this occasion, too, there was a questioning on the part of John’s disciples with the Jews about purification, and they came to John, saying of the Saviour. “Behold, He baptizeth, and all come to Him.” They had heard words from the Baptist, the exact tenor of which it is better to take from Scripture itself. Now, if we ask when Christ was first in Capernaum, our respondents, if they follow the words of Matthew, and of the other two, will say, After the temptation, when, “leaving Nazareth, He came and dwelt in Capernaum by the sea.” But how can they show both the statements to be true, that of Matthew and Mark, that it was because He heard that John was delivered up that He departed into Galilee, and that of John, found there, after a number of other transactions, subsequent to His stay at Capernaum, after His going to Jerusalem, and His journey from there to Judaea, that John was not yet cast into prison, but was baptizing in Aenon near Salim? There are many other points on which the careful student of the Gospels will find that their narratives do not agree; and these we shall place before the reader, according to our power, as they occur. The student, staggered at the consideration of these things, will either renounce the attempt to find all the Gospels true, and not venturing to conclude that all our information about our Lord is untrustworthy, will choose at random one of them to be his guide; or he will accept the four, and will consider that their truth is not to be sought for in the outward and material letter.”
In other words, for Origen, inerrancy only applies to the spiritual horizon of a text, not its letter, history, or external referent. I’m not necessarily advocating this, just pointing out that this is a different approach to what you’ll find in Augustine and Warfield about Gospel harmonization and inerrancy.