That's kind of what is happening, I think. However, the violets remain even after removing the oversaturated blues and reds, so they have high luminance already, just not quite enough to push them into the highlights. So I think that the violets can be fixed with added luminance, whereas the oversaturated reds, and especially the blues, have no corresponding luminance and shouldn't be there. If that makes any sense.

I was thinking about this problem last night, and this morning I realized that it was much simpler than I was making it out to be. It turns out that you could stack as many video layers as you want to get to the correct brightness and then put one more layer on top to remove the oversaturation in the blues and reds.

Do accomplish this, all you need to do is isolate the offending saturation by bringing the brightness of the image down to zero and optimizing the isolation with the gamma level. This essentially deletes everything in the image except for oversaturated colors, and from there you can use the channel mixer to delete some of the red or blue from the isolated colors to soften the effect. Then simply set the blending mode to subtract, and it eliminates the problem areas, and does it better than my previous convoluted method:

Here are some examples without comparison, to save space:

I haven't completely fixed the highlights yet, but it's getting there hopefully.