Even if you decide not to change current course, I would think it is still good idea to visit the prviate school and see exactly what is different and whether it is something that could develop into an viable option if the current situation no longer works.
We visited a local private gifted school a few months ago, thinking that it is most likely not going to be what we will pursue and had our focus on the more traditional path... Until we got the test results and at that same time, DS telling us out of the blue he does not want to go to school. It was so out of the blue (both the results we got and the sudden attitude change towards his class) that we found ourselves frantic with what to do, and ended up completely shifting our plans - ended up applying to the gifted school after all with our son asking us when his school situation would change.
Things can change suddenly... In our case, I feel it was a combination of recent boredom (he loved the class and teacher when he first moved up) and sudden change in how a few classmates were behaving towards him that got to him. So we found ourselves pushed into reversing our orignial positions on things like acceleration and private schools (and whether we would need to consider homeschooling at some point).
