Was the bed squeaky before the horizontal bracing snapped? Because if not then thats your problem. Horizontal sway is USUALLY the problem with squeaky beds, which is why tightening things up helps. But if it's missing that piece, the whole bed will be collectively less rigid, and therefore squeakier. If it still squeaks with that fixed, you could also try adding corner bracing of some kind. Anything that improves rigidity will reduce squeaking.