I recommend having the PiP only covering chat, and not UI elements at all. Don't take it for granted how much viewers like to see the small details - maybe do a small spot detailing the UI design and menu walk-through. Some of us care about those little things as well as the game-play. Maybe only pop your names and twitter handles up when your mugs are full screen, but while playing, utilize the entire screen (or use a scrolling text with transparent BG somewhere unobtrusive). If you check out some of the best streams, you'll see they use a nice border around the PiP frame. Just lends everything that extra pro touch.