Is there a state or property I can set on a prim so that it's visible, but cannot be selected, in the viewport?

No, there is currently no way to explicitly limit the selection this way.

That's what I suspected (and makes sense given how USD is built). Decided to work around it for now by using view states and hou.GeometryDrawable() to get the results I need - works pretty well, minus some snags that I've hit and mentioned in other posts.