I like your thinking on this! I think it would be so perfect for my girl. I'm not too well-versed in Parelli (have his book and done the level 1 stuff, vintage 1999) so I don't know if and how (or where) he goes about teaching sideways towards the handler, but would LOVE to hear & learn about it! Can you tell me more?
(Sorry to take the thread on a tangent.)
As in all things, it it a step by step process. Clearly we are not going to be able to use steady pressure to push on the far side of the horse to help it step over, so we need to be thinking driving pressure. The first thing I do is to get them confident with a stick and flag as a signalling tool. Do not desensitise them to it, we want them to respond sensitively but with confidence to its signals.
Once that is done we then want to be able to do very good sideways away from us using the flag to alternatively drive the shoulder away a step, then the hips, then the shoulder, then the hips etc. This establishes the signal to move whichever part of the body is being signalled by the flag to move away.
The signalling must be done in phases. First a still flag in the correct position, then a lightly waving flag, then however hard you have to wave it, up to and including the flag touching the shoulder or hip.
Once this response is good when standing to the side of the horse, try and stand in front and see if you can drive them sideways whilst you sidestep with them whilst in front of them.
By now the horse is well used to flag signals and now comes the physically hard bit on your arms (You can cheat a bit by standing on a mounting block). Whilst standing to the horses side reach over their back and ask the hind quarters to take a step towards you, going up the phases as I have mentioned. Even if all you see is a weight shift towards you quit. It was a "try" and needs rewarding. Then ask again and keep asking until a little more effort is made than last time, then quit. Each time go up the phases, however keen you are to get the movement don't rush it. Once you have a hind quarter step do the same with the shoulder and so on.
Eventually your horse will come over to you from a distance if you just raise you hand up as though you had a stick and flag in it without actually having one. Hence the importance of going through the phases everytime and quitting on the slightest improvement in the try.
Have fun, I've really enjoyed teaching my horses this and it is a really practical skill. Both for mounting, accurate positioning to load in a trailer and many other occasions it has helped me out. Don't really see what Clinton has against it if it is done not as a party trick, but with a purpose.