This kinda harkens to this fake fic summary in which Shikako simultaneously lives four distinct lives and only her choices are what make them different. So in All You Have to Do (Is Stay), there is a reality which is DoS(ish), one which is her getting overly involved from the beginning (probably ending up with her on a very stressful genin team with Kabuto), one which she takes a half step back and doesn’t want to mess with canon so she gets a team with “extras” (Team Medic!AU!AU), and one in which she goes AS FAR AWAY AS POSSIBLE and joins the Fire Temple monks.
Monk!Shikako is maybe most like what you’re describing, I think. Except in your version, instead of Shikako knowing about the different AUs (because she lives them all) they are all discrete realities and it’s other people who travel across and find her. Which would be pretty appealing as a story, anon.
I feel like, though, that even if she tries to avoid the plot it still finds her somehow. Like, I mean, at the Fire Temple, maybe she and Sora (who is basically a Naruto-Sasuke fusion) become reluctant friends and together they do extracurricular training in trying to control his pseudo-jinchuuriki status, which may or may not help out when Akatsuki comes around? I don’t know.
And I’m also not sure much attachment Fire Temple monks are allowed to have. They’re obviously not the “enlightenment comes from total isolation” but I’m also not sure if, for example, by joining the temple Shikako had to forfeit her Nara status. Most likely she did have to forfeit any claim to heiress (and maybe some cruel and politically inclined rumors suspect that Shikaku deliberately sent his chakra hypersensitive child to the temple so that would be the case) but perhaps she does get to keep some attachment to her family. Even then, she’s probably not the first Nara to join the temple (maybe full time, yes, but Chiriku didn’t seem at all confused by her request for the month-long sabbatical).
What I’m saying is, I wonder if she’s allowed to visit Konoha and accidentally get involved with the plot despite her efforts. Like… since Chiriku used to be part of the Twelve Guardian Ninja–even though that particular organization did not end well–maybe he’s training Shikako to be his successor?
And so she is tasked with “lower risk” guard duty of the Fire Daimyo’s family members–I mean, the Fire Lady canonically hires Konoha genin to catch Tora frequently enough that everyone hates it–or brought along as Chiriku’s apprentice to protect the royal retinue during the Konoha Chuunin Exams. And look how that ended up.
This probably isn’t what you wanted, anon, is it?