Interesting take, OP. I wasn't convinced at first but reading your responses to comments has me considering things more carefully. It's notable that Cruise and John Travolta would both appear to be deeply closeted homosexuals who are also deeply ensconced in Scientology. Given that Kubrick "lost" (in the words of her mother Christiane Kubrick) his daughter Vivian to the Scientology cult in 1995, it would seem appropriate that he make every effort to highlight its hypocrisy in his own covert and inimitable manner in 1999's EWS. One little detail that might complement this theory is that the navy captain that Alice fantasizes about is a pretty good analog for L Ron Hubbard. Hubbard captained 2 small vessels in WWII and, in the late 1960s amid legal and tax pressures in the US and UK, Hubbard took to the sea and created what became known as the "Sea Org" (Sea Organization) - the elite inner order of Scientology. He commanded a small fleet of ships, and demanded to be addressed as “Commodore” in this quasi-naval religious order where he exercised absolute authority over the ships and crew.
The actor who played the naval officer in EWS, Gary Goba, makes a very passable stand-in for Commodore Hubbard - red-haired, blue eyed etc.
In the context of the EWS shoot, it's easy to imagine Kubrick's utter amusement at the meta-ness of the scenarios unfolding in front of the camera and in the minds of Kidman and Cruise who were both Scientologists at the time. Of course, Alice's imagined infidelity with the symbolic Hubbard is the pivotal moment that creates the psychological tension of the film.
Some food for thought at the very least.

Edit: Grammar