Hi Colin. So I’m muting with the palm of my strumming hand but also loosening my grip on the frets a little with my fretting hand.
I learned later from a Metal Rhythm book I’m going through that it’s better to try and use both hands to mute completely and to both loosen and try a full mute. I tried this in my last AVOYP here: AlexisDuprey - Troy Stetina's Metal Rhythm Guitar Vol.1 - Songs 1-6 (around 30 seconds there is a part with rests that require mutes) and I think I’m more successful.