I haven't tried this with an EQG doll, but the boiling water and careful patient prising worked to remove Jem heads back when I used to customise them. I don't think that the EQG dolls are as good quality as Jem, so the necks might be more brittle/prone to snapping with too much pressure. I suspect, though, that this should make them easier to get off? With Jem Hasbro used a separate plastic neck ball which went inside the head and the body and which was glued to the head and impossible to get out of the body without splitting the neck, so prising it out of the head and softening the glue was the only option (like with a pony's neck glue).
I just looked at my Rainbow Dash and it looks as though in her case there's just a ball on the end of the neck and that's inserted inside the head. I would think that would mean you'd be able to prise it off with warm water, to make the plastic expand. I'd just be careful of that neck breaking under the pressure...