I’ve been watching a video tutorial from digital tutors that covers the whole maya to zbrush to maya pipeline, and they mentioned how important a clean UV map is. So I went back to my hydral and looked at the UV map with a little trick they used in the tutorial. They used a checker pattern to give a visual representation of the uv on the 3D model, and low and behold, there were my artifacts. Have a look:

On the left is the model with the normal map, and on the right is the corresponding UV map distortion.

I am now cleaning the uv map, and will be trying Zbrush again. The normal map won’t be very detailed, as I’m just trying to get the process down right now. I’m also going to try another program I found, called Xnormal, and see how that works.