I will build something like this, and if it is too flimsy, add a brace, then push it around some more, and see in what direction it’s too wishy washy, where the next brace should be. On the end, I misstated the brace location, you want it from the floor next to the door part way up the outer arch. If you look up geodesic dome, you’ll see the triangle concept taken to the end.
Your mods may net be as pretty as your original design, but it should work.
