I've got some issues regarding your analysis of the first Piraka-Inika engagement.
Here's a Quote from Hakann, on page 78 of Power Play.
"Hakann looked around the chamber with increasing worry. Avak and Zaktan were down or gone, and the other Piraka were at best deadlocked with their opponents."
Lets do the matchups:
At first, Hakann is waiting for Brutaka, so that he can steal his power. He isn't fighting.
Jaller is fighting Reidak
Hewkii is fighting Brutaka
Kongu vs. Avak
Hahli vs Thok
Matoro vs ???
??? vs Vezok
Nuparu vs Zaktan
(Refferenced solely from Power Play)
1)Hewkii entraps Brutaka
2)Nuparu and Zaktan are taken out of the conflict
3)Kongu defeats Avak
4)Hewkii engages Reidak alongside Jaller
5)Jaller abandons his fight with Reidak, leaving him to Hewkii
6)Jaller engages Hakann
At some point during this, Hahli engages Thok, and at some point, Matoro saves her from his attack. This fight is only in the comic, and is not described in Power Play
Now here's the speculation.
Vezok is the only individual not mentioned at all during the fight.
Matoro is the only Toa who doesn't have an initial opponent.
Therefore, it is likely that Matoro fought Vezok, and it is also likely that Matoro was able to come to Hahli's aid after defeating him, temporarily or not. We know he didn't flee from Vezok, because Hakann's quote tells us that Vezok's best circumstance could have been a stalemate- or worse. Hakann's quote regards Rediak, Thok, and Vezok. Rediak was likely in a stalemate with Jaller, and as Jaller seemed quite comfortable leaving Hewkii alone to combat Reidak as he engaged Hakann- who Jaller thought was leaving.
"Jaller spotted Hakann in the shadows, no doubt planning an escape. He couldn't allow that to happen. The Piraka had to be defeated right here and now and then made to tell what had happened to the Toa Nuva."(79)
Jaller is clearly confident enough in the Inika's victory that he prevents a combatant from exiting while leaving his companion to battle Reidak alone. Jaller is focused on justice, wheras the Nuva were fighting for their very lives.
Of course, Kongu is the wild card. We aren't privy to the exact timing of all the fights, and so it is possible that Kongu defeated Avak whilst Matoro (Presumably) fought with Vezok, and thus engaged Vezok with him, allowing Matoro to save Hahli from Thok. Avak is, after all, recovered and on his feet in time to witness Hakann steal Brutaka's power.
However, Kongu is able to "gulp a mouthful of air before the sphere turned into a vacuum chamber." (76)
Therefore, a notable amount of time goes by with Kongu in the vacuum- for moments before Kongu assaults Avak with his mask, he "calculated he had about four seconds to live."(77)
Because Kongu is able to inhale a large breath of air, the time it took for him to have only four more seconds worth was perhaps long enough for Matoro to dispatch Vezok and save Hahli unassisted. Additionally, Avak only passed out- and one can recover from a choke-hold in as little as three seconds.
The more likely option to me is that, if Kongu defeated Avak before most of the events in the fight had occured, he would have gone to help Hewkii against Reidak, a tougher opponent.
Now for specific counterarguments.
Yes, Matoro had to save Thok. But to say that it's more likely that Thok took out two Toa Inika than he simply ditched the fight in order to catch Brutaka's powers with Hakann? That's unreasonable. Every one-one-one fight we know of skewed in favour of the Inika, and Thok was struggling with Hahli- he was face-down in the dirt when he animated the stone that bound her. Thok isn't known for his combat effectiveness; Reidak and Hakann have both been known to beat him in fights. Thok is known for using trickery and manipulation to win, and it fits with his character as well as the sequence of events that he abandoned his fight with the two Toa to grab power.
I suppose so- but their fight was quick, and neither were able to fully showcase their abilities. Not to mention that Hakann more than held his own against the Toa Nuva.
Reidak was mentioned. And you can't say they weren't defeated, we have no idea what happened to Vezok. Both could have been defeated and revived in time to witness Hakann's and Thok's ascension, just as Avak was.
Brutaka is not a Piraka, and didn't participate in the big fight between the Nuva and Piraka. Despite his irrelevance to the origianl discussion, it is worth noting that he was defeated by Hewkii alone, when all six Toa Nuva lost to him. Different circumstances, sure, but notable all the same.
Defeated by Hakann using Brutaka's power. When the Toa Nuva fought the Piraka, they didn't have access to Brutaka's power. There is no comparison to be had.
This really isn't the same either. Kongu knocks down a bridge and the Inika lose the Piraka. There isn't a big fight like the other instances, and there is almost no combative skill to observe.
The Piraka are defeated when Vezon uses Reidak and Vezok to take out the others. The Piraka didn't last against Vezon for a minute. Vezon even mentions that Toa don't break as easily as the Piraka- and they don't. The Toa Inika are depicted as fighting a long-winded, devastating battle and are successful in knocking the duo into the lava. Of course they only win due to the Zamor. Vezon and Fenrakk were invincible. How else would they have won?
I've saved your first argument for last.
Hopefully, in this colossal post, I've demonstrated that the Inika did, in fact, fare well against the Piraka. The Inika did not "Just survive"; they absolutely castrated them. The fight didn't end when the Piraka found out the location of the mask, the fight ended when the Hakann and Thok stole Brutaka's power, demolished Toa and Inika alike, and forced the information out of Brutaka. When the Piraka fought the Inika with ionly their own power, they inevitably would have lost. something else I've neglected to mention is Brutaka's presence. The Nuva fought six-on-six; the INika fought six-on-seven and still would have pulled a victory.
Finally, and I do mean finally, the Toa Inika didn't have Axonn on their side. But the Piraka did have Brutaka.