1. A basic issue in Gospel harmonization is whether Jesus "cleansed" the temple once or twice.
(Some contemporary scholars call it the "clearing" of the temple, which might be more accurate, but for convenience I'll stick with the traditional designation.)
2. Let's block out the theoretical options, then assess them.
A. Some scholars think it never happened at all. They think the account is legendary of fictional. They take that position because they think it would be impossible for Jesus to singlehandedly empty the courtyard. That's not a one-man job. If, moreover, he did so, that would figure in the charges at his trial.
B. Some scholars simply combine John and the Synoptics. This is called additive harmonization. They think Jesus cleansed the temple twice: first at the beginning of his public ministry (John), second at the end of his public ministry (Synoptics).
C. Some scholars think this was a one-time event. There are variations on that position:
i) Jesus cleansed the temple at the end of his public ministry. The Synoptic chronology is accurate. John relocates the incident at the beginning of Christ's public ministry.
ii) Jesus cleansed the temple at the beginning of his public ministry. The Johannine chronology is accurate. The Synoptics relocate the incident at the end of his ministry.
3. Regarding A, I will say three things: two now and one later (under #4).
i) A number of scholars argue that the incident is on a smaller scale. It probably took place in the South portico. Given the vast size of the courtyard, most folks present wouldn't even notice what Jesus did. This was an emblematic action.
ii) Disrupting the market place wouldn't be a capital offense. So even if the incident had many witnesses, that's irrelevant to the trial.
4. Regarding B, it's certainly possible that Jesus did it twice. That can't be ruled out. However:
i) John records one cleansing and the Synoptics record one cleansing. There's no reason to automatically assume these must refer to separate events. You only get that by comparing John with the Synoptics. Nothing wrong with that. But it's not as if John says there were two, or the Synoptics say there were two.
ii) There are conflicting intuitions on which is more implausible. Some scholars think it's more implausible to suppose Jesus "repeated precisely the same action at the same location with the same attendant question concerning his authority" (Ridderbos). Others think it's more implausible that John would relocate the incident.
An argument against two cleansings is that the authorities wouldn't let Jesus get away with pulling the same stunt twice. However, I think that's a fairly weak objection:
i) The authorities couldn't anticipate that Jesus was going to stage a repeat performance. That was unexpected.
ii) Unless they had minders following him around, they couldn't prevent it in time.
iii) As the Son of God, nobody can stop Jesus from doing whatever he sets his mind to. I'm sure Jesus could be very intimidating or even terrifying if it served his purpose. He's quite capable of staring down opponents.
One argument for B is that an earlier cleansing synchronizes Jn 2:20 with what Josephus says about the terminus ad quo for the rebuilding of the temple.
However, that appeal suffers from complications. Josephus gives conflicting chronological indicators. So there's the question of how reliable Josephus is in that regard.
And there's the additional question of what his terminology denotes. Is he using hieron and naos synonymously, or do they have different referents?
John's own usage is inconclusive inasmuch as we need to distinguish between the narrator's voice and the speakers he quotes.
There's the further question of what the aorist passive verb (oikodomethe) means in 2:20.
There's an undesigned coincidence between the trial of Christ and the cleansing in John. In the Synoptics, his accusers allege that he threatened to tear down the temple. But the Synoptics don't report Jesus ever saying that. Yet Jesus says something like that in Jn 2, although his accusers twist his words.
However, that's consistent with a single cleansing if the Johannine account reflects narrative sequence rather than chronological sequence.
5. Regarding C-i, there's not just a question of synchronizing John with the Synoptics but synchronizing the Synoptics with each other. Mark explicitly says the cleansing took place a day after Jesus first arrived in Jerusalem. Because it was late afternoon, Jesus decided to retire to a suburb (Bethany) for the night, then returned to Jerusalem a day later to cleans the temple.
By contrast, Matthew and Luke simplify Mark's chronology. To a casual reader, the cleansing happens on the same day Jesus arrives in Jerusalem.
It's unclear why defenders of the two-cleansings view think it's okay for Matthew and John to give the reader the impression that it happened on a different date than Mark, but misleading for John to give the reader the impression that it happened on a different date than the Synoptics.
Since Mark is the only one of the four whose explicit about the chronology, while Matthew, Luke, and John are all ambiguous on the chronological connections, consistency demands that we have the same standard for all concerned.
6. Regarding C-ii:
i) In general, John has a more precise and detailed chronology than the Synoptics. So there's no presumption that in case of real or apparent conflict, we give the Synoptics the nod.
ii) Apropos (i), Synoptic chronology is generally simpler. They only record Jesus making one trip to Jerusalem, so that's the only place they could put the incident. By contrast, John has Jesus making three trips to Jerusalem.
iii) However, it's logical that this takes place at the end of his ministry, as the culmination of his challenge to the religious status quo. And the authorities would regard this as the last straw, the final affront.
7. I incline to the view that there was a single temple cleansing, although I don't have a firm position on that.
That doesn't necessarily mean, that John relocated the incident to advance his theological agenda. That interpretation may well be too literary. Rather, he may put it there simply because that's what he was thinking about on the day he dictated that section of his Gospel.
Or, assuming that this is more deliberate, it could be a flashforward, like we have in movies.