The boards across the top will not be a substitute for a corner brace. They will help stabilize movement along the straight line of posts when used with a brace.
Not certain what your set up is but you can run a long post from the bottom of one post to the upper third of the corner post (angle) on both sides of the corner post; l l l/l\l l l -best I can do to illustrate.
This is what we do with locust posts. They are the hardest things to nail and screw into so I pre drill a partial hole. We just nail them on after cutting an angle on the ends.
Not certain what your set up is but you can run a long post from the bottom of one post to the upper third of the corner post (angle) on both sides of the corner post; l l l/l\l l l -best I can do to illustrate.
This is what we do with locust posts. They are the hardest things to nail and screw into so I pre drill a partial hole. We just nail them on after cutting an angle on the ends.