I'm back. Well the situaton has not improved much. Seeing all those pics I see the shirt is shifting around on your body. It has no secure place to hang from.
As you assumed right it might have to do with the neck.
My first question is: Do you have a helper? Someone who can stick a pin into fabric and not in you?
The quickest way to a better fit would be a pinning new the shoulder seams and getting a fitted neck hole.
When we look at your last back pic we see some folds across the back neck - shoulders and more at the right side. (And some bubbles - I do not know where they come from.) Those folds normally happens when there is too much fabric and because there is a Hindrance the fabric can not spread and release the volume (in German Stauchfalten translated: word to word compressed folds). They are not like the pulling folds (german. Stressfalten) when fabric is needed. In your case it means the fabric can't climb up the neck because of your stay stitching.
Now first clip into the the back neck stay stitching first at right side. Put the shirt on. Your helper should now pin the shirt at bust level at right side front and back. Open the right shoulder seam. And remove pin at the back. With the whole hand he should stretch out the back from up from shoulderblade to shoulder and to armhole and from neck to shoulder. Pin and look. As often rinse and repeat till the shirt back looks nice and tidy and CB is vertical and the Bustline horizontal . With chalk mark the back neckhole. (The CB point is a bit over the 7. Vertebrae. It runs along the valley. (If not sure - As I stated before use a thread closed to a circle with a weight - it works!)) He should clip the neck now down to the chalk line on several places. Secure - if possible - with a pin near shoulder of at the bust line again. Now unpick the front pin and direct the front part so that the CF falls absolutley vertical. And pin again back. Look at side seam - it can be that it has swung out a bit to the front. If this is the case you have to open it too. And pin it close again letting out the amount of fabric from front pattern it needs. Now procceed back to shoulder again.
The same pocedure as in back. It can be the case that the front neck will not lay flash with the back shoulder (and vice versa).
Move the fabric till it lay there nicely flat. Pin it over the back shoulder s.a. always adjusting. Clip into front neck till it is laying at the base of the front neck. Chalk the base.
Remove the pins at bust line and look if it stays. Do it then on the left side.
This is something you need a helper for.
And when he are at it: he should check the armpit. If the bustline is the indicator for the Rh then the armhole is too high in my opinion. If you have 2 cm Z for Rh in your draft you should find it there. Use your fingers to check.