There are some excellent points in both Chacha's post (Do you really know there IS another "more nurturing" teacher to be had? What if your son is moved and still does not click with the next teacher?) and Ziggy's post (This may be a crucial teachable moment). I'd say to give both of those posts another look.
Next, you mention that your son and you both spoke to the counselor. Was that not helpful? Did you approach the counselor in terms of "We are unhappy" or in terms of "Help us navigate this and work on resilience"? Maybe you can start again with the school counselor for your son AND for yourself. Talk to the counselor alone first, without your son there. Explain what your son is reporting and note that he is crying frequently. Ask if the counselor has had this kind of issue before with kids who have transferred from Montessori or other programs that are run very differently from public school, and ask what the counselor advises you to say at home to help your son. See if the counselor will meet with your son to work on resilience and taking things day by day, assignment by assignment. Can the counselor make it fun? Some counselors do "lunch bunch" groups where they have three or four kids eat lunch with the counselor at a time , every week for a while, etc., and it's treated as a nice thing and not as "I'm being forced to see the counselor." Bear in mind, the counselor sees kids in stress all the time and has some objectivity that you as the parent don't have. (Naturally!)
Find ways to ensure your son sees that learning is not just about what happens in school. Be sure to get him to museums and doing fun learning outside the school setting (NOT tutoring or Kumon! I mean doing the National Park Service's fun "Junior Ranger" stuff at national parks around you in NJ and NY, for instance, or going to museum kids' events, or setting fun tasks for him--if he likes bugs, help him start a bug collection. Whatever interests him.)
I'd like to add for the longer term: Have you investigated what track your school system, not just your one elementary but the system as a whole, in the grades to come, has for gifted students? I would get busy looking at what the school system has to offer him either this year or next or beyond.
For instance, our county school system here has an "advanced academics program" (AAP) that begins in third grade once students qualify. Children can do AAP at their base school (the school they're assigned to by their home's location) IF the base has some AAP courses available, or they can move to AAP "center schools" where the curriculum is more in-depth, faster and often more creatively taught. Every school system will have a different way to handle gifted student education or advanced academics (a better term for schools to use than "gifted," to me, as it focuses on the aptitude for learning, whereas kids can be "gifted" in many ways that are not academic). You might want to get proactive now and see if there are programs for which your son should be tested or for which you need to apply. I'm referring here to programs already in the public school system, not to private schools etc. Look at your school system's web site for a start.