Isn't neutral just a division of flow between forward and reverse? You never stop the flow so
wouldn't that mean your gate is out of adjustment if your boat won't sit still?
If it isn't down far enough in neutral to stop the boat from going forward then maybe it's just approaching neutral when you put it in reverse.
I had the button out one day and had neutral full time while reving up the engine. It would JUST
go backwards and that's about it.
Sounds like what you have.

But you say the gate is fully closed when it's barely in reverse??? What happens in FULL reverse?
Any thing different? Did you check to see if it pulls the gate back up?