The memory is a bit hazy as to the exact source, but a few years back I saw a video where a developmental professional was giving advice on how to stop young child from screaming, say demands during a tantrum. The idea was that the next time your child has a fit, look at them and hold your hand to your ear like you're trying to hear someone far away and say 'I can't hear you. You have to speak softer so I can hear.' Although it sounds so counterintuitive, I remember, at least, the source was very experienced with degree credentials.
Would any of you with children of this age want to give this one a whirl and see if your child responds to it? Sounds crazy enough to work, huh? Thanks for reporting back your results.