I just wanted to add a personal reflexion:

everybody seems to think that a 'real' (i.e. certificate) Montessori is better than a school labelled Montessori but not certificated. Very often when I say that in our case it is not working I get the question/suggestion that this is because maybe it is not true Montessori.

I do not think this is the case at all, it is more down to the teacher. A teacher who understands the kid and his/her needs is the key, not if the lessons are given to a certain prescription.

And by the way, I am reading the book that Maria Montessori wrote herself and up to now there is not a singel provision for HG+ children. It is assumed that children will follow their own pace, but with the same step-step by step way of learning. She insistes a lot that step 1 MUST be finished and mastered before doing step 2 because stpe 2 uses step 1 as foundation.
I am not finished with it so maybe I am wrong, but up to now this is what I found.

I still think that for most of the children this is one of the best methods of teaching.

The problem is that ours are not 'most' children....