Glad to know those movements were exaggerated and the descriptions a bit off. I suspected they were but just wanted to confirm. Your techniques do work. It seems that the NZ/AASI are more similar.
I used to teach the side slip at my old mountain. It's kinda ironic that the two guys who told "no more side-slip" came out of the PNW.
It was Chris that showed me Winter Park's recommended progressions during new hire orientation. We could adjust progressions to make them our own, but no side-slip. Chris went straight from one footed straight glides with toe/heel engagement to performing traverses with both feet in. Nothing in between. He most definitely made it clear he didn't want to see any side-slipping. My supervisor a few years ago got called aside after he was observed using side-slipping. I've known others to be warned not to do this too.
What I do after the back foot out exercises and the start of both feet in is really a hybrid of sorts. It's a traverse but I'm getting them to do more garland type movements. It's putting the torsional twist in there with the hip/knee/ankle but I don't always mention it. It depends upon the group that I have. They are having a massive amount of material to digest at this point. I'll throw in this info in freeride practice.