I strive to avoid making exaggerated facial expressions, looking at the ceiling and being flamboyant when I play the piano. Additionally, I concentrate completely on the sound that is produced by the piano and I do not play the piano mechanically. I simultaneously focus on tempo, phrasing, dynamics and pedalling throughout my performances. This allows me to channel my emotions through the sound that I produce instead of channelling them through the appearance of my performances. In summary, I strive to avoid all forms of exaggeration during my performances. In my opinion, this is the best way to achieve the highest standard of artistic merit.
Your question being: how do you play the piano? My answer is, per your delineation: I play the same way, as did all of the pianists of the 19th century, as well as most of those in the early 20th century.
Like the OP, I am too busy trying to focus on the particular musicality of a piece (solo or with orchestra) than to worry about the sexual nature of my performance. And, that is what we are talking about here.
Just like some rock star, with their "Cod Piece" to turn on the female members of their audience, classical pianists have long before them catered to the female members of their audience.
Oh gosh, did Lang Lang send out a promotional picture a few years ago showing him dressed in a black leather suit, which was photo shopped to accentuate a rendering of his genitals? Oh, yes he did!
In regards the music critics who encourage/foment this nonsense, I proffer the following personal experience: In the 1980's, I "Ghosted" a review of a recital performance of an upcoming Concert Pianist.
The first half of his performance was poetic, and truly beyond his young 25 years. Then, in the second half of the program, it was all bombastic. It was a totally different pianist, and please remember that this was an audience of Music Majors at an accredited University School.
Adding insult to injury, when he came out for his encore, he returned to his original first half persona, and then played a beautiful Scarlatti Sonata. And in case anyone is wondering, I ripped his head off for "playing down" to his "Music Major" audience.
His initials are YB, and trust me, he will never forget the title of the review "The Banging of Keys" (not my Byline).
Therefore, per the OP, please remember that Claudio Arrau made a very long career out of being true to the music, as well as himself. And, based on the lack of commercial success of the world's great conservatory trained artists, I would strongly recommend the OP's approach.