Oh dear, you are way off in almost everything...
Of course if you expose the paper for longer time, it will get darker, but hey, that is if you have a normal negative! If you have a darker negative, the total light reaching paper when using longer printing time, is the same, given that there is no reciprocity failure. How can you go this off in this kind of very basic principle?
THEN, more dyes mean "darker" image, it is NOT more saturation. If you have an equivalent amount of cyan, magenta and yellow dye, what you have is grey, and if you increase dye density, you have a darker shade of grey. If you then adjust for this by exposing the paper longer, you are where you started.
Dyes ARE the image, they are not some kind of colorants for BW image, which seems to be the basis for thinking in this thread.
The saturation thing has to be explained by different arguments. What I can see here is just misconceptions and new theory around the very basics that are just misunderstood completely.
I would start searching the answer from the shape of the characteristic curve. It would be quite intuitive that contrast - and perceived saturation - would go low when overexposed because of the shoulder area, but the shoulder is quite far up in the modern color negative films and with usual, low-contrast scenes you are not on the shoulder at +1 or even +2 stops. BUT, on the other hand, by overexposing, you move the shadows, which probably are at toe region, to the linear region that has more contrast. This is simple and understandable, but there probably is something more to this that could explain the phenomenon even better. But it is not the fact that you have to expose the paper "longer". The time doesn't matter (unless reciprocity failure kicks in).