Two things concern me. For both of these, I am assuming that the vast majority of students who attend high end private boarding high schools are intending to go on to college or university. If you have no intention of attending university then these concerns would not apply.
First of all, if you change schools and switch to a rigorous private high school (whether boarding or not), you are likely to find a sudden shift in the level of rigor at which classes are taught. If this impacts your grades, this would impact your junior year grades. Junior year is the last full year of grades before university applications are due. This is not a good time to suffer a “glitch” in your grades.
Also, when applying to university, letters of reference are very important. You would be better off if the people writing your letters of reference know you very well. It would be best if they have known you for somewhat longer than one year.
Putting these together, my inclination would be to just not do it unless there is some compelling reason that you have to. You might get something similar to the “boarding school” experience when it is time to go off to university.
We did not look into boarding schools. At one point we looked into a high end private high school. We discovered that they accepted very, very few students entering into grade 11. In retrospect I suspect that there were multiple reasons, one of which might be that this just would not have been a good idea. Instead our kids stayed where they were, did well, did well in university admissions, and did well in university.