I think I have a different take on the neutral grip thing which might help you.
First, pick a stance and refine it. That is where you want to be. Changing stance to a new one when told to is a bad habit to get into with little return. I chased that dog for a while!
What you are looking for is what I call refining the recoil stroke. For starters, look at a GOOD mentor or professional shooter and master their grip. Grip is key. A nice firm grip without shake.
Then work on stroking the trigger in dry fire. The key is a firm grip with a trigger stroke that doesn't move your grip. When starting out, this is a slow increasing surprise break. Master that. Then take it to the next level. Squeeze and know when it will break, exactly. Then faster and know the exact break point. Now, go back to this and focusing on the sights. Break with the sights dead on that light switch or other dryfire target.
Now, use your grip and trigger mastery on slow dryfire. Wow! Are you shooting groups now!
Now, back to recoil stroke. Using what you know, lower the gun slightly below your line of sight and fire 5-10 med speed rounds in a string. See where the gun is recoiling. Move around grip pressure, grip, shoulders , etc until it recoils straight back. Now get back on the sights and watch the front sight bounce up and back down. Adjust grip pressure, arm pressure, etc, until your elbows bend under recoil and a slight tricep push gets your front sight on target. Keep pushing and shooting faster!
Next, using this muscle memory, quit shooting 10 and shift to 5 and then 3 shot strings. Finally, work to master doubles. The doubles will take muscle memory and letting the front sight guide you to trigger the second round.
The key is the recoil stroke being consistent and straight back.