Your problem is in the back... not the neck. Like you mentioned... her topline isn't developed very well.
You might try some flexes and circles. First at the walk, of course. Turn a small circle, pulsing your inside leg, asking her to bend her back. She will want to lift her back and drop her neck if she's doing them right, and at that point you'll want to give softness back to her. Keep her on the circle, but let your whole body feel comfy to her.
Eventually once you got her giving her back when circling to both sides, you'll be able to introduce a signal that asks to drop the head and neck and lift the back.
Keep riding those circles, and let your leg not just keep her out on the circle and giving her nose, but also lift her back.
Once you get lots of softness that way, you can try going straight a step or two. That will involve a little bit of outside rein to get her to move in the straight line, plus that one inside leg asking for the flexed back still.
If you do your work right, I imagine she will respond to that request w/ a dropped neck and an overflexed poll. At this point I imagine you won't gripe about a little overflexing, seeins it's step in the right direction.
But from there you can work out a signal for her to lift her back and drop her neck carriage.