So it looks like quite a few of my potatoes are growing quite well. There are definitely some that did not sprout and grow at all, but that would have happened no matter how I had planted them. A few weeks ago I did spread some composted manure around the top of the hay to give some nutrients to my potatoes. It seems that the ones closest to the manure have grown the best so next time I'll be sure that I spread it more evenly among the potatoes.
What you would do with potatoes planted normally would be to add more dirt on top as the potato plants grow. My plants have grown to the point where they are pretty tall, so what I did next was to layer some more hay around the plants just like if you were burying them the traditional way. So far so good. Now we just have to wait a few more months to see if the actual potatoes do as well as the plants are doing.