Put the current floating hosting info into the activity panel.
Having a random floating bar is very intrusive. The currently hosted channel should be shown in activity (or somewhere, anyway, maybe a dedicated panel) instead.
100% agree that the hosting panel is just in an annoying spot. I wish it would at least save the spot I move it to. I think a good place to put it is over the top or bottom of the video window since the video window isn't playing anything when you're not live (i.e. when you're hosting someone else). That's where I usually end up moving it when it's in my way.