For the vocabulary of pain, escalation might be your best bet for avoiding repetition. Matt's a pretty disciplined kind of guy, given the right context, so perhaps you could start with low-key descriptions?

For instance: he hissed in pain, gritted his teeth, choked back a whimper, uttered a low broken sound, bit back a curse, twitched or jerked etc.

Then after a while: he couldn't stifle a yelp, his voice cracked, he uttered a sharp, pained sound, he cried out, jolted,

And then go for: he screamed, made an animal sound of distress, sobbed, his face twisted in agony, writhed, thrashed, etc

Perhaps finishing with: hoarse screams, his throat shredded, opened his mouth in a soundless scream, broken whimpers, etc

Yelled might be an option, but I don't know when you'd use it. Groaning works as a reasonable synonym for moaning. Especially if you mess around with different framing verbs and adjectives.

...Well, this has been both a fun and disturbing writing exercise. I hope that helps in some way (I also suspect I know which fill you're working on and I am super-keen to read it).