It took a couple more painting sessions for me to feel good about this n0n-objective diptych in black and white. In the first session, I painted over a lot of what I'd added in the previous session. I painted with a brush using titanium white, but left traces of the paint beneath. I've also been trying to put a lot of texture on these canvases.
In my last session, I used a thinner black paint and applied it quickly to give it a "splash-dash" feel, letting the paint spatter a bit along the edges. In the photo below you can see where I painted over in white as well as the final loose "splash" effect in black.