Why aren't you looking at Grado phones? Like Axiom speakers, Grado headphones are very neutral and natural-sounding, and they've been consistent for decades.
The Grado SR80e is about $80 in the US, and has had excellent reviews for years. I've used the SR125 for a long time.
I might remind you that, like loudspeakers, there is little correlation with sound quality and price. Fit is important, of course, so if the phones aren't comfortable, there's no point getting them.
Also amazing are the little Koss PortaPro's, which fold up and are extremely lightweight and comfy. Very neutral and linear sound quality, with slightly overemphasized bass. I have not heard recent models, but they're even less costly now than in decades past. They used to be $50 when they were introduced, and now they're half that.