I don't understand the point, but if you make them both the same material and join them (via Join Geometry), the coincident line between them should be removed - assuming they both exist in the current View Phase and View Phase Filter is set to Show Complete.
There's also a tool on the Modify tab called Linework (LW). Maybe just use the LW tool to make the coincident lines Invisible in the View? Just a thought. A pretty good one, as I've been told in the past. 😉
It seems that no lines for the generic model category are visible in either cut or projection. That would probably address my issue.
Huh? You say "no lines for the generic model category are visible in either cut or projection". What do you mean and how does this relate to your question: "How do I get this cut line to appear in the top layer?"
