Biases/my history: I went to a good public high school after indifferent public elementary and junior high schools. I attended an Ivy League college. My life would have been different if I had gone to academically challenging schools as a youth. I don't know if it would have been better or worse; things have worked out pretty well.

You come off as very smart and self-aware. Still, I think you underrate the risk of ending up as an other-person at the public high school; friends may not be as easy as you expect. Retreating to a public high school may also require explanation to college recruiters.

I also think your conclusion that you would study better with more friends may be a self-persuading effort that there are scholastic reasons to switch. But there don't have to be scholastic reasons: Being unhappy for two more years in your teens is a big deal, and if you are satisfied that your happiness will increase substantially by switching, you should switch. Long view is nice, but part of that view should be that two years of a low-friend existence sounds no fun, and the losses of switching are likely to be minimal.

Finally, commuting is a life-killer. Adults very commonly underrate the loss of quality of life for commuting (I commute 10 minutes each way; I have had jobs with one-hour commutes.) I'd suggest it's even more valuable time lost for a teenager.

Finally finally, I'm confident you'll get this right for you. Take a look at these responses, talk it out, then rock on. Be good, stay well.