What is this type of car called?

True, at one point, earlier, manufacturers did call cars like that roadsters. Later, that term became real grey because they ended up calling cars with soft tops roadsters also. I should have thought of that because before Mopars, I was into British sports cars (roadsters). I suspect that California Cruiser was just a real colloquial term.

There was a thread here very recently, like the past couple months, about shaving the drip rails. IIRC, that guy came to the same conclusion that he didn't like the look, but I think he welded them up somehow so they looked better, and I think it turned out ok. Might want to search for that thread. I think it would be a WHOLE lot less work, safer, and a generally better idea to fix it that way than to cut the roof off. To me, the deciding factor there would be if the car was real solid or not. If not, part it and scrap it, if so, save it.