Coprophagia, poop-eating, is a common dog behavior (but certainly gross to us humans!) There can be a lot of contributing factors, and unfortunately (as with many dog things), there's no hard and fast solution that works for every dog. Naturally, there are products on the market that can be added to your dog's food that will allegedly make her poop taste awful . . . and naturally, this works great for some dogs and some dogs actually seem to LIKE the taste! Go figure. So that's the quick-and-easy solution, but it's not really addressing the roots of the problem.
Sometimes diet can contribute - if the dog is not getting enough of some essential ingredient, they'll try to supplement in any way they can. Check with your vet to identify a high-quality, large-puppy appropriate diet. If she's only getting dry kibble, maybe substitute some wet food. See if there are any vitamins or supplements that might be added to her food. Try to find ways to slow down her eating so that she is able to digest her food properly. Feed her by stuffing her dinner into a Kong, a Kong Wobbler (only dry food), or an interactive food puzzle. Or hide her dinner in several small portions throughout the house and teach her to "hunt" for it - this will slow down her consumption and give her some mental stimulation, as well.
Sometimes, stress can be a factor. Perhaps she is stressed by being confined in the crate, or being far from you. In that case, a simple matter of a remedial crate-training or relocating her crate to closer proximity to you (into your bedroom, or next to your bed) to make her more comfortable could be part of the solution.
Although you said the stool-eating has not been modeled to her by other dogs, in fact, it probably has. Mother dogs keep their nests clean by eating their very young puppies feces. This is how adult dogs teach puppies to keep their living environment clean and soil-free. If your puppy associates her crate with her sleeping and living space (good!), she is trying to keep it clean. Perhaps 4-5 hours is too long for her very young bladder. Try taking her out at 11, 2:30 and 5 instead of 12:00 and 4:30 (or whatever is realistic for your schedule, but is about three hours between intervals).
How does she do with eliminating otherwise?
To help her stop eating her poop in the yard, you could try teaching her to immediately run to you for a treat as soon as she has finished eliminating. You can start by taking her to her elimination spot on leash and standing right next to her with a cookie in hand (hidden if she is too distracted by treats to focus on pottying). Once she has pooped, immediately praise her and give her the cookie. Gradually, increase your distance (still on leash so that you can redirect her attention to you from the poop if necessary) until she is turning away from her poop and running across the yard to you for her treat. Needless to say (and I'm sure you already do this), since she seems quite fastidious and prefers a tidy space, clean up her eliminating area immediately so that there is no old poo laying around to tempt her.
Hope this helps. Like I said, there's no definite explanation or solution that works perfectly for every dog - some dogs just grow out of it after a while, and for some dogs it's a lifelong obsession that simply must be managed by their humans. You'll just have to experiment with different things and see what works for her and for you.