In my experience, when a high sugar content or high CO content soap overheats and starts to show signs it will crack, simply lifting it up off the countertop or work surface and placing it on a rack will stop the overheating. It even works with 100% CO soap in a smaller loaf mold. The added air flow to the bottom surface of the mold cools the bottom of the mold just enough. This has worked for me with smaller size batches and no resulting partial gel ring with soap that heats up.
I have never put a loaf mold into my refrigerator or freezer, but I have seen pictures of soaps in a freezer volcanoing all over the freezer. I would not want to risk that, unless I had a dedicated fridge - dedicated to soap only. The only option I would use for quick-cooling or gel-prevention for an entire loaf of soap would be the garage in winter, as I do use my extremely cold winter-time garage as extra refrigeration for the holidays. The cold concrete would suck the heat right out of the mold and stop it in its tracks!
You mentioned you got the partial gel ring and want to avoid that. And you want deeper more vibrant color. I think you identified the real problem when you said it is a new bag of rose clay. I would suggest mixing the rose clay with a darker clay, maybe Morrocan clay or Brazilian clay, to try to deepen the color and see if you can get the resulting deeper shade of pink that you prefer. If you are against the use of mica, that is. Mica would give you more predictable results, and if you have any on hand, you could at least experiment with the amount to mix with the clay for the desired result.
But if it is for a special order, mica might not be an option (not knowing the specifics of the order), in which case, I'd suggest mixing with darker clay or possibly experimenting with slightly more of the rose clay, although I don't know how much that would alter your result.
You mention there are variations in sugar content in the goats milk at different times (the nature of natural), but is there any way you can predict which contains more or less of the heating elements of the milk? Are you able to determine which milking is less of a heater or more of a heater when added to soap? That might help in preventing over-heating, too. I probably would never really master those kind of nuances, but as a goat owner and frequent maker of GM soap, perhaps you are in a good position to master them and could adjust your process to those changes when they occur.
) In them all, the lye concentration varied from 30-33%. I used different scents in all of them. The rose pretty much comes out the same as a light flesh to pink as Ive only used 1-2 tsps tops in whatever recipe . I may start using more to see what happens. I make magical morphing soap and I think your soap may be magical morphing soap too 
