Your idea of leaving it as Kokorozashi Education with the explanation in brackets sounds good!

In brackets, maybe you can add something like;
Education to help students become self-motivated and active in learning with a goal in mind in order to be independent in the society, and also help them shape the idea of being and living as a whole human being

(Below is the text from the cited website)
「志教育」は「キャリア教育」をさらに広い視野から捉え，児童生徒が将来，職業人や社会人として自立する上で必要な能力や態度を育てるとともに主体的に 学ぶ意欲と目標を持って努力していけるよう，地域社会や企業等とも連携しながら，各教科や体験学習等教育活動全体を通じて，小学校，中学校，高等学校の発 達段階に応じ，人間としての在り方や生き方の探求を促していくものです。

Hope this helps!