Hello, I had the same problem. What I did, because I also saw no other option, is Screen capture (window/screen capture). Now you can transform the screen at "Transform" and then choose the option "Fit in screen". Now you will see your desktop and all that you have on there. So, what I did to make it look professional is using a League of Legends Wallpaper and cleared my desktop. If you can't move your desktop item, then you can sort them by "None" in your desktop settings, instead of having it sort on "date" or "name" for example, so that you can drag and drop your files anywhere. I've made 1 map and putting it in the middle so that it will not be seen by people, because the game menu will cover it. I've hide my down bar menu so that it only opens when my mouse will hit the bottom. The full game screen will take over when you are going into a match.
It is correct that you will see all little screens from OBS, but you won't see that anymore if you are minimizing OBS. Then you will only see the game menu en your wallpaper background.
Now, there is one other problem that I have. My gameplay is lagging when I play the game while streaming on twitch, so I don't know how to fix that part yet. Maybe someone else can help us with that, because you also might find the same problem. The stream is not lagging for the watchers, but my own gameplay is lagging a little bit and I don't know how to solve it yet. Hope this will help you a bit, and I hope someone can help me with that part :-D!