[Ty Ford] “Seems like compression only brings up the noise.”
That’s why whether doing NR before or after normalize, I’d always do it before compression. Give it as little noise to bring. Hope would be that normalize brings up everything and NR then would lose much of the noise too high off the floor. At that point you might have some room on the threshold to keep the noise floor down while compressing.
Unlike the original poster, I rarely run into his situation because, while monitoring, I immediately spot and correct the issue. What I usually bump into is two speakers using a single mic and one whispers while the other bellows. Sometimes you’re not in a situation where you can mic separately. Think of interviewer with hand held mic going back and forth to two people on the street for example.