So, I've been skulking around and I haven't seen anyone talking about Denna's magic.
She explains at some point that she's with Master Ash to learn things she can't learn elsewhere. I think that comes up during the water/stone date near the end where he gives back her ring and she notices the scars on his back. It's when Kvothe realizes that they both taking beatings for knowledge. At an earlier point, in the scene where she gets the three amigos to explain Sympathy in exchange for sexy advice, she asks about a magic that makes things true by writing them down. This happens much earlier, but it's after she meets her patron. Like, she's just learning the concept and is still skeptical enough to ask her friends about it.
The ring return scene also includes a couple instances of her using Yllish story knots in her hair. Kvothe notices it because he's been trying to learn the knots in response to the mystery box, and Denna is taken aback when he notices that her hair knot says "lovely." She then re-ties it as "don't talk to me" and our loquacious Kvothe shuts up for once.
She could've been doing this for a while before Kvothe had the knowledge to interpret Yllish knots. If these knots hold some power, it might explain people's (men's) infatuation with her, considering Bast's admission that he's seen her and she wasn't as super kami guru sexy as Kvothe believes. I also noticed that her suitors are getting much higher class as the story progresses. Ambrose may be a jackass, but he and the guy who gives her emeralds are a huge social and economic step up from our loveable-yet-barely-afloat Sovoy. Plus, she's still playing the suitor game (which Deoch describes like a risky survival strategy for someone with no outs) in spite of having a patron for support. Maybe she has some manipulative hair writing enchantments she needs to practice on unsuspecting nobles?
If you believe the Master Ash = Cinder theory, then this makes more sense because some ancient creature would be the only source for Denna to learn some crazy Naming variant forgotten to man.
Story knots are the equivalent of written language, she's using them to write things in her hair that people will see but she doesn't expect them to understand, she's heard of magic that makes things happen by writing them down, and she's learning some secret knowledge from Master Ash. Therefore, Denna is on a Kvothe-eque journey of discovering powerful lost magics and that's just gotta come up before the end.
So, is there some post out there on Reddit or some ASOIAF forum from someone who noticed this a decade ago with much better references?