We don't really have a good solution at this point.
I don't see any way to use HEX to help. Our GCX could be used after outputs of the Triage to mute/unmute amps (Triage would stay with all amps active) but not only is it a rack device, I think it would be major overkill here.
It is possible that the Triage could be modified to effectively replace the switches with 1/4" jacks... then interface with our Control Switcher to "MIDIfy" your current setup, but I cannot say for certain having never seen inside the Triage box.
Sorry I can't be a better help here!