You'll need two relays per Cannon in order to make them do what you're looking for. The diagram shows a 5-pin relay, but 4-pin relays (without the 87A terminal) will work for this application.
Start by removing your diodes and connecting your Cannon's ground wire directly to a constant ground.
The following is a diagram I borrowed from the12volt.com, on their
page that explains how to convert a ground input to a positive output:
Your "alley" relay will have a ground input (green in the diagram) from the Liberty alley light plug's ground wire and a positive output (blue in the diagram) to the Cannon's primary positive wire.
Your "warning" relay will have a ground input (green in the diagram) from the Liberty corner module plug's ground wire and a positive output (blue in the diagram) to the Cannon's secondary positive wire.
I believe that there is a way to make this work using your diode Y and only one 5-pin relay, but that would be still more complex and probably more confusing.
Your vehicle's horn probably uses a relay. Do you notice any delay from when you press the horn button on the steering wheel to when you hear the horn? While there is a delay, the delay is so minor that it's not really noticeable.