Chiming in somewhat late but feel I had something to offer.
We did the Montessori thing when I worked part time when my oldest was 2. Got pregnant, had another baby, stayed home again. When he turned 4 we wanted to get him back to Montessori, and so we drove 30 miles EACH way to this super nice Montessori school with THE certification, that of course was going to cost us an arm and a leg to go to. On a ridiculous number of acres, gorgeous building, farm where they grew some of their own food that was cooked for the lunches, etc. Sounds and appeared fabulous!
Problem? My son hated it. HATED it. Cried every morning. Would always be fine after we left him though, so we pressed on. 1/4 way through we did conferences and talked about some possible solutions. He's a high energy kid….needs more outdoor/play time, please give him more opportunities to "choose" that work, etc. I could go on and on about this, but long story short, it was a horrible fit for him, he was not happy, I hated the drive, etc. I went to observe him and saw how bored out of his mind he was. I thought that the independence and freedom to choose his works, etc would mean he'd be happier and could focus on his interests more, but that wasn't the case. He wanted to do works that the older (5 and 6 yo) were doing and he (per the teacher) wasn't quite ready for. So he hated the works she limited him too (there IS a focus and a way some things have to be taught in sequence, especially with mathematics in Montessori). Then really close to winter break they told us they wanted him (4.5 yo) tested for ADD/ADHD. So, we told them we were done, would not be returning and I started to seriously think about homeschooling him (I was prepared for him to attend K in the fall). The next week he told me he wanted to go check out the neighborhood preschool where a neighbor boy went, so we went and toured it and he loved it. We also made the choice to not send him that fall to K, but wait an extra year instead (summer birthday) and so he had 1.5 years of pre-k at a school that he adored and he is now a happy, thriving 1st grader at the public school less than 2 miles from our house.
(There's a lot more to it, obviously, like the teacher was a horrible fit for him and the administration had it's own issues and I don't even think they were as Montessori as they should have been (CHILD LED), but what it taught me is that the BEST possible place ended up being the closest/cheapest option to us, and we learned a lot along the way).
I guess my point is what seems amazing on the surface can lose it's luster (for lots of reasons) so making a living location decision based on that would be a really tough sell personally. At a minimum, can you try the school for a year before making a move to see if it will even be a good fit? If it's not a good fit then moving to the better school district would be my vote but then you would know. Good luck!