Got me thinking.....the way you classified the usage is how I think if it, but sometimes I know "that" or "which" just sounds odd in a clause for some reason that I can't really define....so browsed a bit and found this snippet on that/which in relative clauses. It might be a bit old, but it was sort of an "ah, so" moment for me.
§ 62. that. 1. Grammar. The American Heritage Book of English Usage. 1996