Ehhh. I'm really not convinced at all. It sounds a lot like you're grasping a bit to support a pet theory, no offense.
but from her dialogues, it is also implied she isn't the only one doing the judging of souls in Gensokyo.
"Implied" is too strong of a wording, but this is really the only thing I think is worth considering. Either way I don't think that there being more than one judge for Gensokyo even pushes a bit at Eiki being Enmaou.
To note, there being multiple judges would also pretty much mean that any other judge would also be called Yamaxanadu, and that judge would also be exclusive to Gensokyo. As said before, I'm pretty skeptical of Gensokyo requiring any more than the one judge given how small it is. There's certainly a lot of space available where this could have been hinted at more than once, so the lack of evidence (unless I'm missing something) is telling, even though I'm open to the possibility.
Heck, the statement 担当は幻想郷の死者を裁く事で、我々に最も関係が深い閻魔様である "As the area she's in charge of is judging Gensokyo's dead, she is the
most closely-related Yama to us" is some nice evidence against that, unless Akyuu is somehow unaware of there being another Yama judging Gensokyo or she just doesn't care to mention them because they don't get out often or something.
Then, Perfect Momento in Strict Sense expands more about her. In PMiSS, they give her a different title. You view is different from mines in this. You find it odd why she isn't called Enma-o or Yama and I find it odd why she isn't just called Judge of Hell, since it really means the same thing, as far as judging authority is concerned.
They aren't really equivalent quibbles. Having "Supreme" tacked on or not to her title just isn't that important, and is only even slightly relevant at all when assuming your conclusion. The claim that she's one of the Ten Kings, despite her never being called that at all, is quite important in comparison. Clearly we have different views on this, but the key difference is that you're working backwards from a conclusion.
Eiki's traits are special, because compared to other Yama, she is more lenient. This is an excerpt from Reisen's story dialogue:
Eiki: Even if I'm the one in charge of judging you, You will fall to hell.
Eiki's traits are special because she says "even if I'm the one judging you you'll go to Hell" in what's likely an exaggerated threat? I don't think so. I never said the Jizou were all the same either, just that the Jizou turned Yama might be naturally inclined to want people to avoid Hell. Your point was that Eiki is merciful just as Jizou Bosatsu and therefore they are the same; I offered an explanation of that characteristic that holds without assuming that Eiki is Enmaou and still fits with what we're sure of, even if there isn't enough information for me to actually say that these Yama want people to avoid Hell just because they were based on Jizou Bosatsu. My point is that "Eiki is especially merciful" isn't necessarily true and I don't think it's very well supported, and even if it was it doesn't stand as evidence on its own.
Zun is usually vague about lots of things.
It isn't vagueness, it's skipping an entire step in information, and an important one at that. If Eiki was Enmaou and was also a Jizou statue, saying "Jizou were hired to act as many new Yama" and then "Eiki used to be a Jizou statue" is not only confusing, it's deliberately misleading. It's looking at pieces of information that reach an obvious conclusion, and then supposing a new piece of information to that hasn't otherwise been alluded to and concluding something not only different, but conflicting the first obvious conclusion. Like saying P AND Q -> X but then saying P AND Q AND R -> Y, where we don't actually know if R is true, and X and Y are mutually exclusive. It isn't vague, it would just be plain dumb to write that way.
