Now, I hate making assumptions, as we know what tends to happen when one does... but...if anyone can confirm my assumption, or refute it, I'd be ecstatic.

Assumption: A character with a reducer (let's say it's invuln) is dealt 4+ damage. Suppression Field triggers, the damage becomes 3, and then the reducer kicks in and so the character takes 1 click of damage after the reducer.

correct? or incorrect?

Peace machine's power is checked for and triggered after reducers, not when damage is dealt. It specifically references damage taken.

(Special) Suppression Field: If a character would take 4 or more damage, it takes 3 instead.

trait for reference

Page 10 of the rulebook explains damage dealt/taken.