It's tricky in lactic set cheeses because it's hard to adjust the moisture level. Since you are adding some rennet (which some people call a "semi-lactic"), you can up the rennet a bit and cut the curds earlier. So basically as soon as it sets (maybe 8 hours in?) make vertical cuts and then leave it for your total 18 hours. This will help it drain a bit. This will help the rind be less wrinkly.
I would also actually avoid adding any geo to the milk at all. In my experience, geo shows up anyway. Since you've already been growing it in your cave, you'll probably get the same that you've been using, but you may also get your wild version. I like my wild geo *a lot*. It's super dusty and flat growing. Great for the application you have in mind.
I would start off for the first few days (up to a week) at 16 C. This will reduce the humidity, let it dry out and get your cave geo (and other yeasts) going. Then reduce the temperature down to 10 as you were doing. If you can't manage 16 C, then just lengthen the room temperature aging (but keep an eye on it so it doesn't dry out). Once you get white growing on the rind (or anything, really) give it a wash with a 3% brine (3 grams of salt in 100 ml of water). 3% is the salt tolerance for geo, so it doesn't kill it. It just slows it down a bit but also crucially spreads it evenly on the rind. Make sure the cheese is touch dry before you return it to the cave, though. Again, it's totally OK to leave it at 16 - room temperature until it is dry.
It's interesting reading the PDO description (this is one of the better ones I've seen). I feel like I understand what they are doing (though, I've probably not had this cheese -- so take with a huge grain of salt!) That initial 8 days at 12-18 C is done in what's usually called the "yeast room". It's really to keep the humidity down and get the yeasts going. Note that 80% is still fairly low humidity. And then they do another week at an unspecified lower temp. So it's still quite a young cheese.
The other one does 2 weeks at a low temperature (I imagine for draining and protease), then a warmer phase to get the yeasts going. The washes will be to distribute the yeasts. Notice the 24 hour drying period. That's crucial because without it you will get brevibacterium linens growing since the pH will already be in the ideal range for it at that point. B. linens won't grow without a fair amount of humidity, so you'll probably just get some nice, lovely, spicy orange highlights without a washed rind cheese (I assume that's what's giving the hay color your are referring to).
I may give something like this a go myself. I don't have any goat milk, but it should still be delicious with cows milk...
