I wouldn't judge Q too harshly. It might be a bit unfair to say she is "unable to be emotionally honest." She probably had no idea your relationship with Z would affect her as it did, until it just hit her and she had trouble managing what she was going through. Often times our emotions take us by surprise. We think, "Oh sure, I can handle that" until we find ourselves wrestling with inner conflict and we're knocked over by waves of feeling.
I don't think the issue is really about whether it will be a vee or a triad. Q would prefer you not be involved with Z at all, so you trying to make it a vee or a triad is a moot point. It's either continuing both relationships, dropping Z to be with Q, or losing both of them. The fact is you love Q and have strong feelings for Z, and don't want either of those relationships to end. For you to continue with either one of them, Q needs to deal with her jealousy.
Right now, I don't really think there's anything you can do, other than decide whether you'd be happy seeing Q only. The problem with that, however, might be that Z would still be a presence and probably very difficult to not be involved with him. Unfortunately, the two of them are probably going to make some decision amongst themselves, in which you'll likely have no say.
If Q comes back to you and says she wants to continue her relationship with you, but only if you won't be with Z, you might want to ask for some ground rules in order to accept that. Maybe you could say that you would agree not to be with him for a specified time frame, with the goal of eventually resuming with Z, and that during that time Q actively works on getting to the bottom of her possessiveness, improving communication, and you all deal with what's going on.