All of them are affiliated with the Kinoshita Academy in Kyoto under the tutelage of Mie Hamada (Mao doesn't have any juniors competing at Nationals yet), where Cathy is not just a choreographer, but the head coach for ice dance (she (co-)coaches Yoshida/Morita, Kushida/Shimada, Shibayama/Kimura). Kana (during her senior singles career until 2014) and her older sister Satsuki were coached by Mie Hamada and Satsuki now belongs to the Academy's coaching staff, which is why Kana provides choreography for many of the skaters there (e.g. Mayuko Oka, Sumika Kanazawa, Riria Kono, Haruna Murakami, Reina Kawakatsu, Shunsuke Nakamura, Sena Takahashi).
国際大会で活躍ができるフィギュアスケーターの育成をいたします。
kinoshitaacademy.com
国際大会で活躍ができるフィギュアスケーターの育成をいたします。
kinoshitaacademy.com
I agree that Cathy and Kana are both very talented choreographers and that both sides benefit enormously from these arrangements. I also agree that each choreographer has their own "personal voice", shaped by their individual influences and backgrounds, instead of there being overarching national styles (at least nowadays).
If we compare the choreographies of for instance Kenji Miyamoto, Akiko Suzuki, Mihoko Higuchi, Misao Sato, Cathy Reed and Kana Muramoto - are there really enough common characteristics to determine a "Japanese style"? I don't think so. In fact, when you're familiar with a choreographer's style, you can tell just from seeing one of their works in many cases. Mayuko Oka's "Peacock" for example just screams Kana Muramoto (who was/is majorly inspired by Canadian Shae-Lynn Bourne btw).
Well, the MF Academy is very new indeed, but Kensuke has been coaching since 2011.

His coaching career has really taken off since he took on the role of head coach at the Academy in 2021 though, which is truly remarkable. If you're interested in his background and how he arrived at being offered the position at the MF Academy (which he did not found himself), there are a couple of interesting articles/interviews about/with him chronicling his path and shedding light on the development of his coaching philosophy:
日刊スポーツ・プレミアムでは、毎週月曜日にフィギュアスケーターのルーツや支える人の信念に迫る「氷現者」をお届けしています。シリーズ第11弾は指導者編として、中庭健介(41)の来歴を辿ります。2011年に現役引退後、福岡を拠点に指導者としての道を歩み始め、2021年からは千葉県船橋市で「MFアカデミー」のヘッドコーチを務めています。2022-23年シーズンは、渡辺倫果(20=TOKIOインカラミ/法政大)や中井亜美(15=TOKIOインカラミ)らが活躍を見せ、中庭コーチの指導にも注目が集まりました。全3回の「中編」では、29歳まで競技を続けた理由と、指導者として歩み始めた当初の苦悩を描きま...
www.nikkansports.com
Welcome to Absolute Skating, information site for and by the skaters and their fans. The place to meet the person behind the skater and experience events on and behind the stage.
www.absoluteskating.com
(The Nikkan Sports article is under paywall though.)