I actually spread it angled like that, and cull it angled like that, then, once it's on the bottom, I finally twist it right. The spread provides an ample amount of cover, so it's fine, and looks cleaner.
i think you should just practice. otherwise you can use the clean up method as a triump, sort of like an inverse somersault-esque move using a deck flip of your choice (casually just flip it over or TG Deck flip, etc)
I personally use Chad Nelson's perpindicular reverse ( action described in " Fourplay"-Surfaced) which is basically a perpindicular cull with a reverse so that when I close the deck I end completley clean- no reversed card.