To answer all the questions, I believe I should start with the most relevant one first.
>If it's the Throne God's power that prevents the contender from reaching the Throne, then what is the
evidence that each layer of singularity depth equates to a hierarchial transcendance
This is particularly because the Singularity is stated, multiple times, to have variable size depending on the strength of the ruling deity. Aside from the fact that weaker gods normally can't reach the bottom no matter how much they try being used as an evidence, the structure's size is always being compared. This is the case with Yato comparing Hajun's Singularity to Mercurius - saying that the former sits within the depth so extreme that it would be completely unreachable/endless when compared to Mercurius'. (Note that the Singularity always represent an infinite abyss of transparent Taikyoku, it is infinite in size even If a God with, hypothetically speaking, 1 Taikyoku occupies the Throne) This is most likely referring to Hajun's being ontologically superior, from an unknown degree, to infinite or beyond depending on how it is interpreted. Likewise, Mercurius' Singularity, as pointed out in Marie's route by the perspective of the Gods themselves, would be perceived as endless compared to even 10 Taikyoku lower, this is supportive to the former claim.
As for why do I believe that using a perspective statement (referring to the one above) from such route is apt - This is particularly because the gods are the ones who paint over all things, altering creation to their whim, this applies to even the Singularity, which will be filled by the successor god occupying the Throne and altering its depth regardless of size as a necessary mechanic of the system, be it stronger or weaker one.
Furthermore, there is also another instance that is fairly supportive to this, and that is Yakou Madara, who at that point was also a "Singularity", (an actual one, with transparent taikyoku) attempting to eradicate Hajun. As Yakou Madara was attempting to reach the Throne - in which he could do so without hindered anything thanks to his special nature, he pointed out there there are "steps" down. Each of the step required him to "ascend" and guide himself to becoming a "deeper existence" due to the increasing complexity (mainly from the presence of colorless Taiji inside, which represents nothingness and encompasses "vast information" of creation) or else he would go "blank" or diffused. These steps correlate to the depth of the Singularity.
Even among the gods, strength is tied to "depth" of their essence/soul/atman. A god with "deeper universe" would naturally be more powerful. While this doesn't really mean much, it is still quite contributive to the quotes above.
To be quite honest, I think that this is most likely enough to support, or at least heavily imply the argument that the Singularity can indeed have hierarchical layers/transcendence within, and with the Gods being capable of painting it and the rest of creation alike as long as there is no similar opposing force, this seems to be enough.
As for the scans, the vast majority of them are already either in my two previous CRTs and Blogs that were used, you can mostly find quotes along with context or translation there. (Inserting them on phone is a pain in the buttocks, so please spare me ;-
@
GLHF22
There will always be more questions in the future unless I finish revamping the explanation page, which should already be renamed "Shinza Banshou Explanation Page", by the way.