Hmm, I don't really buy the theory that the colors of Gaius represent Misato wishing for Shinji and Asuka's relationship to work out. Gaius represents the Earth and humanity's collective will to continue as they are, in other words it represents all Lilin forms of life's will to keep on living. Shinji and Asuka don't really factor into that.
Not only that but if that was true, surely the vibe between Shinji and Asuka at the end wouldn't be "it's true we had feelings for eachother, but there's too much baggage so this is goodbye, thank you". Gaius would certainly have been messing up its mission if that was at all part of it.
In my opinion the spears represent broad fates/destinies/wills that have been passed down. A lynchpin of Gendo's plan was to rid the world of all 6(?) that were passed down by God (it seems Cassius represents Seele's hope to take the place of the angels and all copies of Longinus represent the angels' fate to wipe out the Lilin). By getting rid of the two fates passed down BY God, only Gendo's will remained in the anti-universe to shape reality using the Golgotha object, but they saved the day by artificially constructing a new one to override his will with a more divine alternative that with the help of Shinji turned the tide.
The anti-universe is susceptible to strong wills so by giving Unit-01/Shinji (a power equal to Unit-13/Gendo) a stronger will than Gendo's human/Nebuchadnezzar will, Unit-01 had the advantage (with the help of Shinji convincing Gendo he was wrong).
I basically see it as using a special key to start an engine/car. In the presence of a stronger key, which transferred the will of all Lilin, their wishes were able to be granted by Shinji.
Anyways all this is to say that I think the point is its the collective will of the Lilin/Gaia, and Las doesn't come into it, especially because if it did they wouldn't have ended their relationship. (Plus programming in a wish that effects a human relationship seems kind of like it'd be against their will which doesn't seem right).
Anyways even so thank you for posting the theory. I know you didn't write it and even to the one who did I don't mean this critique of it personally. I just think it's kind of missing the point of the thing.
Edit:
Anyways, to contribute a bit to this thread, I thought I'd share that I noticed on a rewatch that when Shinji sees a vision of Quantum Rei, the moon is "healed"/normal in the background. IMO this has some significance and even though it doesn't have the same blood streak from at the end of EoE (aka one similar to the one it had in Rebuild), this represents how Quantum Rei is the same one that was created in EoE.
My reasoning for this is that even though we do see the mannequin headless CGI Reis created in 3+1, if any of them were meant to be the explanation for Quantum Rei in 1.0 (same spot as NGE ep1), 3.0 (observing Rei Q in LCL) and 3.0+1.0 (watching over Shinji at the lake), then I feel like they would have behaved and acted like the previous hoard of Reis from EoE, but they didn't. Rather they were just reformed Eva Infinities/FoI's, and didn't teleport nor reap souls for Instrumentality. In addition they just don't look like Quantum Rei, who is 2D animated and still has a head on her shoulders.
Since 3.0+1.0 didn't demonstrate an alternative creation of Quantum Rei, IMO much like how Kaworu has repeated the cycle since NGE, Quantum Rei has as well. Rei is more passive than Kaworu, so the way she uses her existence through all time and space in every alternate world is just to be an observer. Whereas Quantum Kaworu tries to actively "fix" Shinji/make sure he gets an outcome that brings him happiness. The metaphorical meaning of him failing every time is that Shinji must reach his happiness himself and by his own will, you can't just force someone to be happy.
Also even though Kaworu says he's fated to repeat the cycle forever, I don't think that really contradicts it being his own will that started the loop. Firstly in EoE Lilith and Adam merge so Kaworu logically retains both fruits, meaning he now has in some form an independent will and "knowledge of good and evil" in addition to the godly power to use it, so I believe he would be able to initiate his own fates/wills at that point. Additionally, Evangelion (both NGE and NTE) has a consistent theme of people forming destructive cycles, sometimes even by nothing but their own wills, even when they know better.
Therefore I don't see Kaworu lamenting his continual repeating fate as implying he didn't start the cycle, since so many people know they are stuck doing the same thing over and over again but feel like they can do it right "this time". It takes Shinji to snap him out of it. Additionally his speech about music and "playing over and over until you're happy with the result" is definitely a metaphor for not only Shinji's continual battle with depression but also Kaworu's self imposed cycle.