I had a similar experience as a child. I cried every day morning before school. This continued until I was switched to another school.
Both schools were regular ones, and in both cases - there wasn't any bullying. I don't remember what the problem was, but the fact is that going to a different place had a great effect.
In your particular case, it could be the change itself that had an impact, rather than the "Montessorinness" of the new school. Also, consider the Hawthorne effect - it could also explain the situation.
Looking back at those times, 30 years ago, I really cannot tell why I didn't feel well in the environment managed by with my first primary school teacher. She was a decent lady, she treated her pupils with respect and never shouted at us, or anything of that sort.