There are a few new juniors at Peddie every year, and I am sure that is the case at many schools, and they seem to slip right in with no issues. I am sure the non-cliquey and friendly, yet tight knit, culture at Peddie really helps.
I remember refuting your impression of Peddie as a STEM/sporty school in a post last year. I’d be happy to answer your questions if you would like to DM me.
I don’t know your exact situation, but to your first question of “is it possible to transfer as a Jr and have a good experience,” I agree with @AnonMomof2.