Back three is all my all time fav trick!! It was a pain in the ass learning it but I mostly practiced flat... as you described the board often goes 360 shuv while the body randomly does a 360 to follow the motion. to get rid of that issue, what I thought of is to go for it a 100% BUT thinking that as soon as I'll land, I'll revert the remaining "degrees"... just tricking myself into leaving the board under my feet in a way. Other I did is practicing alot the bs 180 that are fully done with the back foot. I watched alot of greco too..
As for taking it to the stairs, I practiced going parallel to the gap, curb whatever, then slowly starting facing the gap the "normal" way.
a hella fun trick!!!!!