Well, as per the Headline: Do Adept Ways count as Qualities for calculating the limit?
As far as I seem to remember from the Missions FAQ, Adept Ways are handled like Martial Arts in that they are "not really Qualities", as in, they don't become more expensive during play.
I know Surge and Infection don't count for Qualities, but those are pretty unique and different.
It's never been a problem for me with Priority because where should that Karma come from.