Like some others, I can certainly see the writing on the wall and am ready for a strategic vote. To tell it true, I'm not overmuch disappointed in this outcome; we do have quite a lot of domain space right now to utilize, and it will be quite some time before it begins to fill up and make us regret our hasty grab for power.
Let's look at Ling Qi's foundation Domain slot right now:
A lot of people are focusing on the ally-buffing part, but I see two other big things. First, the most significant mechanical bonus is spiritual defense, and second, there is an additional bonus that can assist in both social situations and against certain types of checks. Granted, perception checks are included in that.
But one thing that strikes me is that Ling Qi has made a habit of dealing with Spirits quite a bit. I think it wouldn't be unreasonable to say she's had the most dealings with Spirits of anyone in the first year, including the monsters. She has patrons like Zeqing and Xin, she bound Sixiang, and even many of the jobs she took involved interacting with spirits and pacifying them. CRX hired us to be her Spymaster, but Ling Qi has developed this relationship with Spirits all on her own.
When dealing with Spirits, obviously one wants spiritual defense. When dealing with Spirits, often there's an opportunity for discussion before things come to violence, even if the situation is scary. After all, Zeqing is a terrifying blizzard spirit, but due to Ling Qi's diplomacy and tact in her interaction with Hanyi Zeqing has invited her into her own home and even shared her potent offerings with her.
Now let's look at the option I'm voting for:
[X] Internalize Argent Mirror
-[X] Ling Qi receives a four die bonus when attempting to discern lies or see through illusions.
I think this actually shares a lot of properties with that. Illusions seem like a thing to commonly watch out for with Spirits, and such alien creatures often have inscrutable motives, so knowing truth from lies (even lies they tell themselves...) can be especially important.
Ling Qi seems willing to welcome Spirits into her home, as they have welcomed her into theirs. Perhaps she will become the girl who strides the gulf between the world of Spirits and the world of people, with a little of herself making a home in both, or even with her home striding that gulf as well, with all the necessary safeguards and accoutrements to make it so. A girl who deals with the mystical and alien as if it was commonplace, and who becomes a bit mystical and alien herself in the doing.
My future domain leanings will probably continue along this path, emphasizing the Spiritual world, spooky things beyond the ken of humans, relations with the alien, and so on and so on.
Mechanically, illusions detections are a perception test. So for your avowed goal, the reroll is simply better.