The "mounting" of the front fender shown in the picture I provided simply demonstrates how far away the fender is from the wheel even at its closest setting (without having cut the stays). Because of this distance, the fender won't fit under the head tube/fork at all, which is why I wasn't able to mount it correctly.
I don't understand why the fenders can't come in further. Back when I bought my last pair, it was possible to loosen the nuts on each stay, slide the mounting bracket down the stay, bringing the fender in closer to the hub, and sliding the mounts around the fender to wherever they needed to be. Get everything arranged just so, tighten the nuts on the brackets, cut the stay, and you're done. Has SKS changed their mounting so this isn't possible?