This is the most realistic account of what could have happened.
The only gap I see so far is that Sow Belly Brownie doesn’t look to me like he has a bone-breaking punch in him. Yeah, he’s a full grown lard ass but that doesn’t mean he’s strong or quick. I have much personal experience putting lead bottoms like him on their backs and hard knuckles and high arm strength is rare.. While he might have thrown some haymakers my suspicion is that he slammed the Cop’s head in the door and that would more readily explain a broken cheek bone?