Man, I was hunting for these last week and ended up just bouncing between the big sites. I get a decent amount on AO3 if you're willing to sift. The tagging system is a lifesaver—you can filter for 'Fox Kit,' 'Kurama's Child,' and 'Naruto Raises Fox' and it actually pulls up stuff that's on-topic. You gotta ignore the weird crossovers that slip in, though.
My biggest gripe is that a lot of authors seem to start strong with the kit's first appearance and then lose momentum, turning it into a generic power fantasy. The best one I found recently was 'Foxfire and Shadow,' where the kit's abilities are tied to sealing and it creates a whole new dynamic with Jiraiya. It's slow, but the author updates monthly.
Honestly, I've had more luck with older sites like fanfiction.net, weirdly enough. The search is awful, but the stories from the mid-2000s have a certain charm. There's less focus on romance and more on the found family trope, which is exactly what I'm looking for with this premise.