Yes, that way has worked for me fine. It is a good way, imo. I do it in a slightly different order than you, but I've trained Brandy to back up by my legs, too.
Here's how I do it: I first say sssss, sssss, and sit deep, then I use my legs to motivate her feet, then if I have to use the reins I will. I've gotten to the point now where I hardly ever have to use the reins at all. If anything I only have to slightly jiggle them, with no pressure. (Btw, I say sssss instead of back because then nobody can tell you are even saying anything. My riding instructor taught me that; she used to show in Western Pleasure all the time).
I like how Clinton Anderson does it too, I'm a big fan of his. I do it his way on the ground. And in the saddle too, actually, I just changed it a teeny bit.
**I must not forget to thank the difficult horses, who made my life miserable, but who were better teachers than the well-behaved school horses who raised no problems.**