The problem is that you have three identical components that all use the same remote command (remote control codes are just numbers). The only way to solve that problem using a single remote control is if the remote supports assignable emitters so you could have Cable1, Cable2, Cable3 and each device 'mode' sends the command to a specific emitter that is attached to a specifc component.
If the Monster remote cannot do that, then you are SOL. Remotes from Universal Remote, like the MX-350 and above, can do it.