Would it be possible to tear this godhood from Morrigan's body?
Well, I think it depends on what we all think "godhood" means in-setting. I, for one, don't think that Mythal or any other entity is a "god" in any meaningful metaphysical sense. They're clearly powerful entities, but I'm not even convinced they're something other than elves who have very strongly modified themselves with magic.
But in any event, the practical answer has to be yes. Flemeth clearly removed it in the first place to pass it on to Morrigan. There has to be a way of replicating what she did, even if it is difficult.
Hellfire. This is why I needed to be a blood mage; I could just take the knowledge from Morrigan's mind after she drank from it. As it is... we, the elves, need this knowledge, and Morrigan is by no means a trustworthy keeper of it. But if the Creators betrayed us, I don't want to be bound to their will. Again, blood magic would have been so useful here.
Morrigan is a blood mage herself. I don't think it would be quite so easy to poach and raid her mind. More importantly, it's not entirely clear if that knowledge is in her mind in the traditional sense. You hear voices if you drink from the Well (from what I can tell; I've never made a character who'd drink from the it, as even my Dalish are quite the dissents and otherwise atheist) which suggests the knowledge, while a part of you, isn't in you (or yours) in the traditional sense.
As to the elven gods, from what Solas has to say about them they weren't really much into sheparding the elves when they were around in the first place. Since (IMO) what likely happened was that Solas used his power to raise the veil and separate out the Fade (which had the side effect of nerfing elven magic, locking away the surviving gods (if one subscribes to the theory that Mythal was betrayed before that event), and stripping the elves from their ageless youth, i.e., their quasi-immortality) and this shut out the "gods" from their followers.
I don't think they can be blamed for being outplayed by Solas but, at the same time, I don't think the elves would want them back to be ruled over by them.