You a very correct about a fork brace doing all those things and more. That's why major conversion companies recommend or put them on.
When I had my 2 wheel older Goldwing, that's one thing I did was to put a brace on the front end. Really stabilize the front end's wobble.
Did you take photos, if you did, please post them on how to, or let us know where the video is about installation.
Thanks
Rosy
The video is on YouTube. Just type Black wing fork brace installation.