The extruded cut tool is designed to only cut solids, so you're not gonna have much luck with that.
To get the desired effect, try using the "Trim Surface" command instead. It's essentially the same tool but for surfaces.
Thanks! This did work, but then I realized that I could do the planar surface feature as part of a boss extrude, so I ended up doing this, deleting the planar surfaces I didn't need anymore, and extruding through the new solid.
I feel totally stupid for not doing this to start.