Opening Safari to "Full Page" every time.

Yes. Open Safari in Full Screen mode and leave it that way: Use apps in full screen on Mac - Apple Support

There is no need to routinely quit apps.

Note that WheelieNick deliberately said "drag the edges of the window out as far as they will go" This gives you almost full-screen (except the MenuBar stays).

Dragging the edges of the window forces Safari to store that size as the default window size. Clicking the button DOES NOT do that.

Yes, there is. Simply drag the corners of safari so that the window fits your entire screen. After that, close safari and start it anew, it should open in a full page window