I main Peacock and Bigband so maybe i can help you.
But about Big Band,He have a lot of tools to counter Peacock zoning but the main thing you need to do is...keep the pressure on peacock on the first seconds of game,This is not just for Big Band its for every char,run on her face dont let them get away to begin her zoning game. And if she begins,you need to find the little gap on her zoning and use your tools to counter her, defend her projectiles and see her pattern and punish her, Giant Step [H] destroy all projectiles on the screen and knocks her, you can use j.HK and tech forward to close the gap between you and her, another cool trick is cancel s.HK into Brass Knuckles [H] so you can hit full screen.
If you need help on training and stuff add me, i think i can help you.