I realized that while I have a brayer, I don't really have a good surface for rolling out the ink. In class there were tables with glass taped down to them. Perhaps if I bought a small piece of plexiglass I could recreate that setup. But for now I decided to brush fabric paint onto the block with a foam brush. After testing it on a scrap of paper, I decided I was ready to move onto some fabric.
I used this baren to push down on the linoleum to get an even print.
The first one came out a bit too light, so over the next few I tried adding more ink, putting more weight on the baren, and holding it down longer.
Here are the last two prints. While not totally perfect, there is marked improvement--and I don't think this method will ever yield perfectly smooth lines, as any fabric has a texture.
Here's the final piece. While it has its imperfections, I nonetheless have some (somewhat) grand plans for it.