My opinion is that v. 34b is redactional, but that v. 34a is integral within this unit....Compare the similar block in Luke 11:49-51 which attributes the whole block to "the Wisdom of God":
Matthew 23:34-35: "Therefore I send you prophets and wise men and scribes, some of whom you will kill and crucify, and some you will scourge in your synagogues and persecute from town to town, that upon you may come all the righteous blood shed on earth, from the blood of innocent Abel to the blood of Zechariah the son of Barachiah, whom you murdered between the sanctuary and the altar. Truly, I say to you, all this will come upon this generation."
Luke 11:49-51: "Therefore the Wisdom of God said, 'I will send them prophets and apostles, some of whom they will kill and persecute, that the blood of all the prophets shed from the foundation of the world, may be required of this generation, from the blood of Abel to the blood of Zechariah, who perished between the altar and the sanctuary.' Yes, I tell you, it shall be required of this generation."
So the material in v. 34a was present in the copy of Matthew or Q that Luke used. I also think that it is apparent that the form in Luke is the more original of the two: (1) The attribution to "the Wisdom of God" is unusual, indicates a citation of pre-existing scripture, and elided in the Matthean version, (2) the assonance between apostelóeis "I will send" and apostolous "apostles" in lost in Matthew, which also expands the "sent ones" into a three-fold list, (2) in the second clause "crucify" replaces "persecute" to give the citation a more contemporary Christian pertinence, (3) the second clause also has a shift in person to "you" to better adapt the scriptural citation into the rest of ch. 23 (which addresses "you Pharisees"), (4) then Matthew adds v. 34b into the passage which derives from Mark 13:9 = Matthew 10:17 and the unique material in Matthew 10:23, (5) then the next clause alters "blood of all the prophets" to "blood of all the righteous" which harmonizes with the mention of Abel, who was not a prophet, (6) the following clause embroiders the mention of Abel to "innocent Abel" and similarly clarifies the bare mention of "Zechariah" as "Zechariah the son of Barachiah," and (7) the final clause again changes the person to "you" in harmony with the modification in (3). So if Luke preserves the original form of the passage (which apparently is itself a citation of an earlier text), the reference to "Zechariah the son of Barachiah" is secondary and interpretive.
I think the evidence is pretty strong that the reference was originally to "Zechariah the son of Jehoiada the priest" in 2 Chronicles 24:20-21. The strongest evidence imho is that the language in the passage and ALSO in Matthew 23:37-39 = Luke 13:34-35 is allusive of 2 Chronicles 24:17-25, suggesting that this -- or more likely a targum of it -- was the scripture that was being cited:
2 Chronicles 24:19-25 LXX: "And they forsook the house (egkatelipon ton oikon) of the Lord God of their fathers, and served the sacred poles and idols. There was wrath upon Judah and Jerusalem on that day, yet he sent prophets to them (apesteile pros autous prophétas) to help turn them to the Lord, but they would not listen. He testified to them, but they did not obey him. And the Spirit of God came upon Zechariah the son of Jehoiada the priest, and he stood up above the people, and said, 'The Lord says this to you, "Why do you transgress the commandments of the Lord? You will not prosper since you have forsaken the Lord, and thus he will forsake you (egkataleipsei humas)." ' They then plotted against him and by the order of King Joash stoned him (elithobolésan auton) in the court of the Lord's house (oikou). So Joash, forgetful of the kindness his father Jehoiada had shown him, killed Jehoiada's son, 'May the Lord see and avenge!'. And it came to pass after the end of the year that the host of Syria went up against him, and came against Judah and Jerusalem .... and God gave into their hands a very large army, because they had forsaken the God of their fathers; and he brought judgment upon Joash. When they departed, they left him a very sick man, and his servants -- plotting against him to avenge the blood of the son of Jehoiada (haimasin ton huion Iódae) the priest -- murdered him in his bed. So he died, and they buried him in the city of David, though not in the tombs of the kings".
Luke 11:49-51, 13:34-35: "Therefore the Wisdom of God said, 'I will send them prophets (aposteló eis autous prophétas) and apostles, some of whom they will kill and persecute, that the blood of all the prophets (ta haima pantón tón prophétón) shed from the foundation of the world, may be required of this generation, from the blood of Abel to the blood of Zechariah (haimatos Zakhariou), who perished between the altar and the house (oikou). Yes, I tell you, it shall be required of this generation .... O Jerusalem, Jerusalem, killing the prophets and stoning (lithobolousa) those who are sent to you! How often would I have gathered your children together as a hen gathers her brood under her wings, and you would not! Behold, your house is forsaken (aphietai humin ho oikos), And I tell you, you will not see me until you say, "Blessed is he who comes in the name of the Lord" ' ".
Note also that the defeat of Jerusalem at the hands of the Syrians is punishment for the murder of Zechariah, just as judgment of "this generation" and "Jerusalem" will be required to pay for the "blood of the prophets shed from the foundation of the world". Further evidence that the "Zechariah" in question is the son of Jehoiada can be found in rabbinical sources, which claim that the blood of Zechariah could never be washed out of the Temple and that when Nebuzaradan entered into the Temple in 587 BC, he found this blood on the floor which bubbled up and learning that it was the blood of a prophet who had to be avenged, Nebuzaradan was assured that he would have victory and the bubbling did not cease until the fall of Jerusalem was complete (cf. Taanith 69:1-2, Sanhedrin 96a, Targum on Samuel 2.20). This tradition compares very well with the synoptic allusion to the blood of Zechariah and its connection to the coming destruction of Jerusalem.
A third major piece of evidence of the Prophetarum Vitae (thought to date to the first century AD), which ends its list of prophets with "Zechariah son of Jehoiada". Similarly, Zechariah is presented in the synoptic logion as the climax to the succession of prophets and it has been suggested that this reflects the Hebrew OT canon in which 2 Chronicles comes at the end of the Ketuvim. The passage on Zechariah is also very reminiscent of the synoptic material:
Prophetarum Vitae 23:1-2: "Zechariah was from Jerusalem, the son of Jehoiada the priest, and Joash the king of Judah killed (apekteinen) him near the altar (ekhomena tou thusiastériou) and the house (oikos) of David poured out his blood (exekhe to haima autou) in front of the Ailam [= the porch of the Temple], and the priests took him and buried him with his father. From that time visible portents occurred in the Temple, and the priests were not able to see a vision of angels of God or to give oracles from the Dabeir [= inner sanctuary], or to inquire by the Ephod, or to answer the people through Urim as formerly".
Luke 11:49-50: "Therefore the Wisdom of God said, 'I will send them prophets and apostles, some of whom they will kill (apoktenousi) and persecute, that the blood (ta haima) of all the prophets poured out (ekkhunomenon) from the foundation of the world, may be required of this generation, from the blood of Abel to the blood of Zechariah (haimatos Zakhariou), who perished between the altar (thusiastériou) and the house (oikou)' ".
Here we see a number of other similarities, including a reference to blood being "poured out" and the location of "near the altar (thusiastériou)" which is absent in the original text in Chronicles. A reference to the altar (mqdsh') is also found in the Targum on 2 Chronicles 24:18.
So if the original reference was to "Zechariah son of Jehoiada", the author of Matthew bungles things by making him the "son of Barachiah". This of course was facilitated by the bare "Zechariah" in the earlier version, which left his parentage open to question. The form of the name is suggestive of the more famous prophet Zechariah (cf. Zechariah 1:1), but no martyrdom tradition exists of this individual (cf. the Vitae). So the suggestion seems pretty good that a reminiscence of the individual mentioned by Josephus (BJ, 4.5.4) may be in play here. The main problem is the variable spelling of the patronym in the MS tradition of Josephus: we have Bareis in P A V R Lat, Baroukou in M1 and C, and Bariskaiou in L and M2, neither of which is Barakhiou (the name in Matthew 24:35) tho Baroukou comes a little close. Perhaps the variability is due to influence from Matthew...but which direction? Was Baroukou original or was it Bareis and the other name represents an assimilation to the name in Matthew (with Bariskaiou being an amalgam)?
We know the reference to Zechariah in Matthew posed a significant exegetical problem in the early second century AD because an alternative explanation was offered by the author of the Protevangelium of James, that the Zechariah in question was the father of John the Baptist (24:1-4).