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I would go with not having her be an Eihei. I don't personally like the addition of Eihei to SAINT and think for being a trainer she does not need to be an Eihei.
I was going to mention the Eihei thing being unlikely unless you — the GM — specifically wanted it for your plot, but you already covered that. Everything else looks good. I'm fairly certain that conditioning wasn't a thing until YE31 when it was OOC approved, but it doesn't matter enough to remove the part about the character getting it in YE26 so Kim can decide how/if she wants to change that mention.
SAINT field operatives and Tokutenku SOFT soldiers are usually either NH-33S or Type 33A depending on their personal preference or mission needs.