I know this might be a pain depending if it's a lengthy segment, and just how much/often the level is changing, but you can try several (3?) levels of Broadband noise reduction, and edit between those where appropriate. Not the fastest/simplest nor the most elegant, but might work depending on the material.
The only other (slightly crazy) idea crossing my mind at the moment is trying to key in on the noise while avoiding the content into a sidechained compressor bringing it back to a steady noisefloor, sort of try to undo the AGC, de-noise, and then apply any dynamics needed to resulting file, but the odds of this solving more than it fixes, or avoiding tons of compression artifacts are probably 0.
Are they focusing on fidelity or audibility? Is this music or speech? Broadband, focused etc. Maybe post a sample?