I'm really impressed when I see the horses sidestep either towards the handler or away from them on TV. That stuff is hard when you have reins and legs on them and they are making them do it with a halter and rope only. Getting there will take some time, but it would be so cool!!
You'll be surprised at actually how quickly some horses will offer moves like that once they get to "following feel" and you learn to read each other. My little guy and I were working on sidestepping away, and on a whim I tried flagging the stick under his belly and ckicking as I walked backwards, and he sidestepped three steps toward me.
It was probably a fluke, I haven't been able to replicate it since, but shortly after that I left for school and haven't gotten a chance to work much more at it.
Remember, it's all a progression, built on a foundation. Groundwork and dressage (and all training, really, but NH groundwork and classical dressage seem to emphasize it more, IMHO) put a lot of focus on having a solid foundation and building from there. Not intending to take away from the skill and experience it takes to train a horse for any discipline, most can be boiled down to a very
general set of steps that is tweaked to suit the needs of the horse in question. Dressage has the training scale, Parelli's 7 games have a definite progression. CA doesn't exactly have a concrete "Exercise #1, #2, ...", but there is definitely a recommended order to the tasks. You and your horse will get there, I'm sure.
I definitely think that NH has a place in the dressage world. Maybe not to revolutionize... I don't think we'll be seeing GP Freestyles done in rope halters, but to complement, especially in the groundwork department.