I heard in a shiur from Harav Zelik Epstein ZT”L the following explanation which may shed some light on your questions. (Any errors are mine alone and do not reflect in any way on Rav Zelik, ZT”L).
First, what is the significance of “Invisinuso,” “his humility,” how does humility play into this? Of course, we have Rash”i who explains this word as “Savlanuso,” patience.
Harav Zelik ZT”L explained this word in light of the gemarah in Sanhedrin which states that in Dinei Nefoshos (capital cases) we begin “min hatzad.” This is a euphemism for starting with the least learned Dayan. Why? If the greatest Dayan in Sanhedrin were to state his opinion first, the others would not have the temerity to state a dissenting point of view — all would echo the p’sak of the godol. Thus, in order to avoid any undue influences, in a case of Dinei Nefoshos, the Sanhedrin would first hear the opinion of the most junior members, working up to the most senior dayan.
R Zechariah b Avkolus was, in fact, the greatest member of Sanhedrin at the time. When the case of Bar Kamtza came before the Sanhedrin he should have given his opinion last, in accordance with “poschin min hatzad.” However, Rav Zecharia b Avkolus was a great “onov”, a humble person who did not think of himself as the greatest in the Sanhedrin. Thus, he insisted on being seated “min hatzad,” among the ranks of the least learned. As a result, his opinion was elicited first.
So when he rejected the idea of killing Bar Kamtza for having introduced a “mum” into “kodshim,” (“they will say anyone who introduces a mum is liable to the death penalty”) all the others fell into line and gave the same psak. For, after all, he was, in reality, greater than them all despite his protestations to the contrary. Thus, his Anivus contributed directly to the destruction, since it caused his voice to be heard first and the death penalty rejected. (Ad Kan).
So in answer to your question, the second judgment, whether to execute Bar Kamtza was the actual core reason for the destruction since the decision to spare him allowed his return to Roman authorities and the resulting events. The prior case, bringing a blemished korban, was a precursor that explains the situation that Sanhedrin faced.