I've used stearic acid at 1% in soaps recently and they always go through a complete gel without any help. I agree that the problem is overheating, probably a combination of the stearic acid and the sugars in the milk. I also noticed that your goats milk is noted as 'evaporated' which means that it is more concentrated than fresh goats milk. I only make goats milk soap once a year, and I have to use the stuff from a can (I don't have access to fresh here, no one local sells it). When I make the soap I use about 3/4 of what I really want to use and add the remaining as water. My reasoning to add more water to the evaporated milk is that when evaporated, the milk is more concentrated - there are more sugars, proteins, etc. to react during the soapmaking process.
My advice: ditch the stearic acid, it's going to heat up too much even if you put it in the fridge/freezer and you're going to burn your soap. Check how much water you're using with your recipe - as Old Hippie asked, did you replace 12 oz of water with the goats milk or add in addition to the water? Your water to lye ratio is 2.73:1, which might be ok if you are replacing part of the water with milk. I usually soap at 3:1 water to lye ratio for swirling and coloring techniques. For a plain soap such as this I would go down to a 2:1 ratio, or even 1.5:1.