I use both of those, actually, because they make sense in my routine. I start with the ring on my index finger, use Ring Thing, take it off, slap it onto my ring finger on my right hand, turn my hand over, pop the ring through my finger, put it back at the end of my ring finger, slide it down then pop it over to my pinky finger, lift my hand up to eye level, pop it through my pinky, toss it to my right hand, vanish it and show it back on my left index finger where I usually wear it.
I also started doing some random stuff like pulling it through the side of my finger a la Reflex, and swallowing the ring and pulling it out through my throat. etc.
I use some of the information from De'Vo's De'Ring as it does teach how to handle a ring smoothly, not only the 'De'Ring' trick.