I like your theory and it inspired me to muse a little.
As Nick is the only character in the story with any real character arc, I think it’s safe to say that he’s finding himself through the story and possibly trying a few different things, including exploring his sexuality, which he may have had to put on hold during the war, and certainly as a youth, growing up as a member of a prominent family in a small city.
If you’re right about Nick, then the description of Jordan Baker as being physically androgynous fits with your view. She was,
…a slender, small-breasted girl with an erect carriage which she accentuated by throwing her body backward at the shoulders like a young cadet.
But Nick’s promiscuity — the men, girl from Jersey City, the girl back home — throws Gatsby into relief.
Gatsby, for all his lavish extravagance, the opulence and flamboyance of his lifestyle and his questionable business morals, is a one-woman-man.
In his relationships, Gatsby is the most righteous character in the book.
So, Gatsby, with all the question marks over his character, is true to one woman, while Nick, “The most honest man I know”, is true to nobody.
I think, if someone has to tell you they are honest, they probably aren’t.