I thought you might reply.
I looked at the H&H video where they make a DR. 6:50 in you'll see the square cut head and the top strap being sunk in. Then the square mortise you are worrying about.
Lots of blacking and tapping.

The thing to remember is that these shotguns are machine made. There's a machining order that allows their quick manufacture.
Some have no draw between the plumb cut and the shoulders of the action, so the fit between them should approach perfection. Or they pound themselves.

Out there doing it best I can.