The only way to take away the advantage of people with headsets is for the game to have no audio at all. I can capture a video of gameplay of all the CODs, going over various surfaces, put it through Audacity and then use a programmable headset to filter out other sounds to have my own self-built Amplify if I wanted to. You'd have to get the developers to make a silent FPS to end the Dead Silence v SitRep/Amplify debate once and for all.
LMGs make short work of the dog so it might be worth looking into using them for the smaller maps.