I have two children in Montessori and agree wholeheartedly with the above.
I would like to emphasize the check for AMS or AMI. Any school can all themselves a Montessori school, so I'd make sure it's at least certified in one of those two (not familiar with SAIS so cannot comment on that).
Similarly, I’m curious as to what the details of a “slightly less generic” type system entails.