I just joined this group and saw this post. My thoughts may echo those of others. My older son, now 12, had an absolutely wonderful exerience in a Montessori primary school his kindergarten year (he turned 5 in September of that year). I thought Montessori was a good fit for him, and if there had been the opportunity he'd have been in a Montessori school sooner. I never told the teachers I thought he was gifted, but they figured it out pretty fast.
They let him work at his own pace, and while they encouraged him to explore different areas they didn't coerce. They did ask all children to finish one material before going to another, but "finish" meant work to what the child perceived as a stopping point then put the material away. (I wish the putting things away when he's done lesson had stuck!)
When I observed the classroom in the middle of the year (through a one-way glass) some of the younger kids were spending 5-10 minutes on a material and other kids were working on the same thing the whole time I watched. Some were working together, some alone, and some working alone would stop to talk to each other or look at what others were doing, then go back to work.
The teachers actually had to make an exception to the rule for my son because several times during the year he gave himself projects that would last several weeks (they could leave mats out overnight). He was allowed to leave one of these projects to work only on materials set up for two or more children, then come back to his own work. I don't think that was a pre-existing policy -- but the teachers were flexible enough to see that it was appropriate and wouldn't seem unfair to other children. He really did have a goal in mind for when a project was "finished" and wouldn't stop until he reached it. I see that as a good lesson -- better than dashing something off for an arbitrary deadline even if it's not really done.
So I'd also see the "checking things off" as a red flag. Even in a large Montessori school teachers should be able to circulate and see what children are doing. They should be able to see and note which children give up on a material when it gets hard and perhaps suggest an easier material or else offer encouragement to stick it out longer -- but still let the child make the call. They need to be asking themselves why the child isn't "finishing."
As you probably know, "Montessori" isn't a copyrighted name and there are several large organizations with somewhat different approaches that train and certify Montessori teachers (as well as some schools that don't have Montessori trained teachers at all). Most Montessori schools allow parents and prospective parents to observe the classroom, sometimes from behind a one-way glass. If you can do this at the school you're looking at I think a lot of your questions might be answered. Look at the kids and look at how the teachers are interacting with them -- and ask questions if you don't understand what you see.
Also, my understanding is that Maria Montessori thought it was a good thing to have a large number of kids with different abilities and personalities in the classroom and also to have children of different ages together. That was part of the learning experience. It's easy to draw a distinction between "play-based" and "academic" preschools. In a good Montessori school, in my opinion, the distinction should be somewhat blurred. The kids should feel they're playing (albeit with some rules/procedures) and the "work" shouldn't be coerced on them. Maybe like the kind of workplace where it seems the adults are actually having fun . . . .
As for after Montessori -- I did end up homeschooling my son in the third grade (second in math) because he was so far ahead of even what gifted programs offered. But that may have been him and not the Montessori school. We moved away from the town where he went to kindergarten and more Montessori wasn't even an option. The Montessori teachers had been concerned at the midyear that he wasn't doing enough math, but as a sixth grader last year he went to national MathCounts and had the state high scores on two levels of AMC tests (8 and 10). Their patience let his interest in math come when he was ready -- and paid off.
Hope some of this helps.
