Amy why not just grate a small amount of sweet potato and add it to one of the hash browns just before you shape and cook it. That way it won't get the first cooking. If it works then you will know for the rest.
I made these yesterday they tended to fall apart a bit as it turned them four times, the last half I added an egg and a little rice flour to,the mixture it is so much better held the shape beautifully. Nice taste ate four in a row. Piggy piggy.