I thought I was following those steps pretty darn close. I have to go back and see where I failed. I think when he got fidgity and tried "flight mode" I pulled him to keep him from moving putting him in "fight mode". Although at the time he reared when backing up I was just putting slight preasure on the halter and when he didnt move tapped his chest with the stick. I may have someone record my next session with him so I can learn better and see his body language and responses better. Study him in a sense.
I'm very glad that you had success with his old owner/trainer. An inexperienced owner and a horse who has learnt rearing gets him out of work is a combination that always scares me, and if not dealt with quickly, often ends verybadly for both horse and handler.
From what you wrote above, it seems to me like the root of the problem is the same as 99% of rearing. The horse is confused, being asked for movement, forward is blocked, so in his mind, the only logical thing to try is up. It doesn't start out as nasty. It is simply him trying to figure out what type of movement you are looking for. It happens exactly the same in the saddle; Asking for movment while blocking forward = The horse trying up to see if that is what you are asking. Once you backed off after the rear, he thinks "I went up, the pressure was removed. That must be what she was asking", Hence the repetition of the behaviour. The subsequent removal of pressure (out of fear, perfectly reasonable in someone not experienced with this) is simply confirming in the horses mind that it is doing the correct thing. It is the removal of pressure that teaches, not the application.
I think the main thing you need to do now, is ensure you have a failsafe 'forward' button. If you get behind his hip and drive him, he needs to move forward, NOW, and keep moving until you move back to a neutral or blocking position. A horse can not rear when they are moving forward. I would leave backing completely alone until you have a controlled, immediate forward depart when you move into a driving position, and then further, a controlled whoah when you move back to a neutral or blocking position.
The backing... Ah it is so often the cause of problems! I dislike the idea of you staying stationary while trying to 'drive' the horse backwards away from you. Especially when teaching. To me it is a very aggresive way of teaching somethign that is often confusing. The way I teach a back up, is by firstly getting a solid knowledge of leading on my horse. They need to follow at my shoulder, turn when I turn, and stop when I stop. The aim is for the horse keep you at his shoulder, wherever you are. If the horse rushes, change direction. It is similar to teaching a dog to heel. Once I have a good stop, I will start to teach the back. I will stay facing firward, but march backwards next to my horses shoulder, while putting a little pressure on the halter/bridle, and a little pressure on the chest with my hand. The horse by now know to keep my at his shoulder, so generally without much trouble, they back along with me. Eventually you wean them off the halter pressure, and then off you backing, so they back in response to a light touch on the chest, and in my case, a cluck. If you are set on having a horse who will back of a wiggled lead, or with you standing a metre in front, then now would be the time to incorporate it.
I wish you luck!