You might want to re-consider HQ/QW if you are thinking of Fate. They are not that different conceptually. But, let's talk Fate.
So, I think you probably don't want to add too much extra game mechnics. If you are thinking about using stunts for magic, for example, you have to consider if the standard three stunts are enough for you. Either you step up the abstraction ladder and maybe use the runes instead, or you use whatever mechanics you already have, like Aspects. I'd suggest the latter. Let me talk through how I would do it.
I'd probably say you should all have a High Concept and a Trouble as per Fate Core, and then I'd say that if not part of your High Concept, you have a mandated Cult and a mandated Culture Aspects. You probably then will use your Cult Aspect and a skill to do common magic for a lay member, and a initiate or a devotee spend some of their Stunts (if their High Concept allow it) on specific magic effects. You can then narratively decide how powerful magical effects a lay member or initiate can do by just boosting (common understanding of the term, not the Fate game mechanic) your skills with the Cult Aspect. Maybe limit an initiate to one magic stunt, or do it all according to they story.
When a devotee Create an Advantage and they act out their cults belief and mythic stories as to hero form, you have an excellent opportunity for a Scene Aspect.
I think Fate Core could work well in Glorantha that way. Oh, yeah, you might want to rename some of the skills...