I'm a mainstream teacher and have written a whole-school behaviour policy using 123 Magic, for a school in inner-London jam-packed with children with ADHD, many with EBD and a number of children with ASD. We used it as a way of improving consistency across the school in terms of responding to unwanted behaviour coupled with raising the profile of the reward system we used for acknowledging and rewarding desired behaviour - both were used for all children regardless of any additional needs but were supplemented by extra reward strategies for those who needed it.
One of the major successes was with reducing the emotional involvement in sanctions for unwanted behaviour. We went from members of staff 'having a go' at children by saying, "X that's a warning because you've done this, you've done that, I'm fed up of blah blah blah" to reducing the attention given for pre-defined, unwanted behaviours to, "X, that's 1".
The time saved meant teachers could get back to teaching more rapidly, other children's learning wasn't held up by an argument between adult and child and it also meant that adults actively looked for the positive behaviours to reward because they could be more gushing about those (now being limited when 'telling off'). The giving of a 1,2 or 3 was referred to as a reminder (of the thing that was being done that was counter-productive to learning) and a simple tally mark went on an A4 chart by the teacher's chair - every child's name was on this in alphabetical order so children could visually track how they were doing in terms of reminders. Session lengths varied according to the age/needs of the class and each session started afresh.
Using 1,2,3 magic across the school was reinforced in the playground and in each classroom by provision of a 'blue zone' (blue mat/spot, blue table and chair, blue bench) in every space so that once children had been 'through' the 1,2 and 3 they spent some time apart from everyone else on/in the blue zone. Time out depended on child's age.
For the vast majority of children it was very successful and I'd love to put it to use in my current school (but I'm not responsible for behaviour here) as I think the tracking element, the non-emotional reminder system, pre-defined STOP behaviours, consistent approach across setting and personnel can be incredibly effective for all children but especially children with ASD for whom random systems and vague adults all wondering in with different approaches and tolerances for disruptive behaviours is far from helpful.
It does need to be coupled with a strong reward system though; I cringe whenever I observe systems (usually in schools) that draw attention to unwanted behaviour with great enthusiasm but fail to couple it with a reward system.
I'm not sure my reply has helped you as a parent but I thought I'd share it anyway!