I have some confusions regarding the calculation, as well as some issues. But first off, here's the excerpt from the official translation:
I had no fear.
The void that filled my enemy was nothing short of a black hole, but I had swirling galaxies born of a multitude of prayers within me.
The hue of the dark-purple lightning shooting from Gabriel’s eyes and mouth gradually began to shift.
From purple to red. To orange. To yellow—and then to white.
Crack, went a faint noise, and a tiny fissure ran through the liquid-metal body surrounding the Night-Sky Blade.
Then another. And another.
More white light poured from the cracks. The base of the six wings extending from his back began to glow with fire. Where his mouth opened wide with laughter, it began to crumble and lose definition. Holes appeared in his shoulders and chest.
Beams and curtains of light were shooting out of every crack running all over Gabriel’s body, and still he did not stop laughing.
“Ha-ha-ha-ha-ha-ha-ha-ha-ha-haaaaaaaaaaaaaaaaaa…”
His voice grew higher and higher pitched until it was nothing more than a metallic whirring vanishing from hearing range.
The great dark angel’s form was entirely covered with white cracks—and in a single instant, it compressed, imploded…
And released.
An explosion of light on a gargantuan scale formed a spiral that shot upward to the heavens.
As for my concerns, for starters, I am confused as to why we are talking about draining sunlight, as the scene does not have anything to do with the sun, or overblowing Gabriel's body in Underworld with spatial resources.
It is a mere act of streaming all the memory data into his brain for processing. Think of your brain like a CPU. It has a standard clock speed. It has a safe overclock speed. And if you try overclocking it manually beyond the safe limits, it is going to start burning itself.
Kirito's attack is not making Gabriel explode. It's the amount of data being streamed to his head that makes his fluctlight fry out. And the explosion is basically his real fluctlight collapsing under the weight of all that data, it's not an outcome of Kirito just feeding the body in Underworld energy for it to explode. That's why he implodes before launching upwards and exploding. Because his brain is receiving the Mnemonic Data at first, his brain keeps "feeding" on the data, until it can no longer handle it.
Looking at the actual explosion is interesting. I generally would not look at the Anime for references. Of course, it's a bit of a necessity in some cases when there are no clear descriptions, however these this bit attracts my attention:
An explosion of light on a gargantuan scale formed a spiral that shot upward to the heavens
So first off, whatever the explosion was, Kirito did not face it head on. It literally "shot upwards" rather than exploding on Kirito's face. Anime portrays this as "it explodes and then something shoots upwards", whereas the way it is written, it feels closer to "The explosion created an upwards spiral".
Secondly, the explosion itself. The Anime uses a traditional explosion effect, however the description is interestingly not "an explosion" but an "explosion of light". In Underworld, as we discussed there are no "Light attacks", however there is one literal "explosion of light" that exists within the system. It has quite the low level requirement for it too, as it is one of the most basic combat skills.
"Generate Luminous Element" followed by a "Burst Element". This creates a literal "explosion of light" which is 100% harmless on a physical level as the light has no mass to hurt anyone, it is one of the best tricks in combat, used to blind your opponents. Again, the Anime takes so much liberties in this scene, like it's Gabriel's explosion shooting up getting rid of the black cover on the sky created by the Night Sky Sword whereas the sky clears up slowly as Kirito puts the sword back in its sheath, the sky cover being much higher that it has clouds underneath in the Anime whereas in reality, the cover was below clouds close to the ground etc. So I am on the side of approaching the Anime's depiction in a questionable way.
And you have caught onto a key detail in your approach as well that factors into this. Kirito shows no signs of being hurt
at all. He simply gets up as if nothing happened, not even a scratch on him or his outfit. And as you stated, we have 0 mention of an incarnate shield too. Now of course, it could be that Gabriel's Fluctlight gave away before all the resources were depleted, so Kirito would have been able to heal himself, but his statement makes this seem unlikely:
When the light of the stars vanished, so did the energy that was filling my being, and I floated in an exhausted state, face up to the sky.
The left arm that had been cut off and disintegrated was back on my shoulder.
"It was back", that's a phrasing you wouldn't use if you healed yourself. So I would put that down under subconscious incarnation. Even the Blue Rose Sword is in his hand, which was otherwise held by Eugeo during the final portion of the fight.
However, that still leaves the issue of "tanking the explosion" if we assume it is an actual explosion, and not just a burst of blinding light. No shield, low on health, running on mental fumes at that point, along with still heavily living under the weight of all his guilt. On top of this, the explosion happens after he achieved his goal, to prevent Gabriel from capturing Alice, so there is nothing left in him that would push him to survive without him realizing, he has no subconscious motive to manifest such a thing. On top of this, he has no armor that would protect him, and he is still shy of top human performance age of late twenties, so even as a human, his HP is not at its highest yet. He can heal himself to a certain extent, sure, but he has no reasonable way at all to tank a blast if we assume that is an actual explosion, which just gives more legitimacy to the mention of "explosion of light". Also, healing himself would actually heal his wounds, but not necessarily his clothes. Throughout her fight in the ruins, Asuna consistently heals herself, same as Leafa against the onslaught. They get rid of their wounds, but their clothes remain tattered (which the anime showcases in multiple occasions but does not stick with it, as it is costly to have heavily modified clothes animated as you must track all the tatters to all the movements at all times etc).
All in all, as I always say, look at how its behaving and not what it is stated as. And to me, it sounds more reasonable in this case that it was a weightless blast, rather than the typical explosion the Anime showcased. It even matches how bursting Luminous Elements function. I can even go and mention Luminous Elements are the healing elements of Underworld, which I'm sure would make a possible connection of Kirito getting his arm healed quite clear too, although it cannot be explicitly claimed to be the cause due to the books not mentioning it.
But again, a lot of puzzle pieces land in the correct places when going by this assumption, compared to the other alternative, that leaves a lot of question marks unanswered.
Again, it is quite the vague scene and I am not exactly sure how you guys would want to go ahead with it, but seeing how even the smallest mentions made it clear that Fanatio's attacks were not light attacks, I just tried to provide as much as I can in hopes of you being able to reach a conclusion.
