I'm well aware of what those units are. I've done professional audio and video work for two major TV production networks--Discovery and PBS--and worked as an intern for two audio production companies before that, done live audio reinforcement for three theater production companies, and do audio work casually for fun-- so please don't dismiss my comments offhandedly.
If the mixer preamps are clipping to the point where they are going into circuit protection shutdown, then yes, a cheap preamp-limiter circuit WILL prevent that from happening. A limiter circuit like the one in those units is not particularly amazing sounding, and it will still distort, but it will distort on the front end while outputting a relatively consistent line level voltage reading.
I didn't dismiss your comment offhandedly, I gave it a serious response. No need for the CV.
I said "compressors operate on line level signals, so you would need an external preamp". You said "that's not true, look at these compressors (which are actually preamps that feed into compressors)". My point was just that in order to compress the signal, you still need to boost it to line level. The devices you linked me to do just that, but they are still external preamps and don't contradict what I said.
It might be possible using one of those preamp/limiter boxes to turn down the preamp gain just enough that the louder passages don't clip, but are still detected and reduced by the compressor. The compressed signal could then be amplified by the mixer preamp, simulating greater headroom (at the cost of reduced signal-to-noise ratio). Might be worth a try.
Edit:
A limiter circuit like the one in those units is not particularly amazing sounding, and it will still distort, but it will distort on the front end while outputting a relatively consistent line level voltage reading.
Fair enough. I was thinking more along the lines of trying to get rid of the distortion completely, but it's true that this would stop the mixer from cutting out. I don't think we disagree with each other.